LOAF: Load and Resource Aware Federation of Multiple Sensor Sub-Networks

Wireless sensor networks (WSNs) serving in hostile environments are susceptible to multiple collocated failures due to explosives, and natural calamities such as avalanches, landslides etc., which could partition the network into disjoint segments. A similar scenario is encountered when autonomous WSNs need to collaborate for achieving a common task; therefore, federating the segments or individual WSNs would be essential for sharing data between them. The federation may be achieved by populating relay nodes and providing perpetual inter-segment paths. In this paper, we tackle the federation problem while considering constrained relay availability that makes the problem more challenging. We exploit the use of a limited number of mobile relays to provide intermittent inter-segment connectivity. We propose LOAF, a novel algorithm for LOad and resource Aware Federation of multiple sensor sub-networks. LOAF strives to group the segments into multiple clusters considering the amount of energy consumed to support the inter-segment traffic as well as proximity between segments. The formed inter-cluster topology is star-shaped where the segments in each cluster are served by a distinct mobile relay and a central cluster provides inter-cluster data delivery. During forming a central cluster, LOAF opts to balance the load on the individual mobile relays in terms of energy consumed in travel and in wireless communication. We analyze the properties of LOAF mathematically and validate its performance through extensive simulation experiments.


I. INTRODUCTION
WSNs have attracted increased interest in recent years due to their numerous civil, scientific and military applications. In a WSN, a large set of sensors are deployed to form a mesh topology and coordinate their actions to carry out a common task [1]. Thus, the inter-sensor connectivity has a significant influence on the effectiveness of WSNs and should be sustained all the time. Moreover, a WSN often operates in harsh environments and may suffer from a major damage which results in simultaneous failure of multiple collocated nodes and causes the network to get partitioned into disjoint segments. For example, in a battlefield, parts of the deployment area may be attacked by explosives and some nodes The associate editor coordinating the review of this manuscript and approving it for publication was Kashif Saleem . get destroyed. Restoring the connectivity among segments is essential for enabling full network operation. Another scenario is when autonomous networks are to be federated in order to aggregate their capabilities and achieve an emerging task such as search-and-rescue, military situation awareness, criminal hunting, etc.
Federating a set of disjoint segments or standalone networks has recently received growing attention from the research community. Most published solutions exploit the deployment of stationary relay nodes and formulate the federation problem as finding the locations of the least relay count to form a stable inter-segment topology [2]. In other words, a connected topology is formed by populating sufficient relays to provide stable inter-segment data paths. However, resource scarcity makes the federation problem more challenging. In this paper, we consider the situation where the relay count is not sufficient to form a perpetual topology; instead multiple mobile data carriers (MDCs) are employed to form intermittent communication links among the segments. Particularly, we solve the federation problem when the MDC count is so constrained that it is not feasible to assign an MDC to each link in a minimum spanning tree of the segments.
Given the MDC availability constraint, each MDC has to serve more than two segments. We thus ought to divide the set of segments S into multiple groups or clusters. This is mapped into a set cover problem which is NP-hard. Therefore, we pursue heuristics. While grouping segments in multiple clusters, we opt to balance the energy consumed by the MDCs for touring the segments of the individual clusters and uploading/downloading data over wireless links. We propose a novel algorithm for LOad and resource Aware Federation of multiple sensor sub-networks (LOAF) by forming a k-clustered topology where the energy consumption overhead in touring and data transporting is balanced among the k MDCs. LOAF consists of two phases.
In the 1 st phase, LOAF first tries to find the energy-based center of mass of S while considering the inter-segment data volume, hereafter denoted as eG. Basically, to calculate eG, LOAF considers the in/out data volume for each segment S i and calculates the corresponding energy consumption for up/downloading data at S i via wireless communication. Based on the found eG, LOAF opts to form (k − 1) non-central-clusters C i 's around eG while minimizing the overall energy consumed in visiting the segments of C i , i < k by an MDC i . During the 2 nd phase, LOAF opts to form a central-cluster C k around eG while balancing energy consumption among MDC i 's, ∀i in terms of travelling a cluster and transporting data. The clustering results in a star-shaped inter-cluster topology via which every pair of segments in different clusters can exchange data at most within two cluster-hops. LOAF is validated through simulation experiments and is shown to outperform competing schemes.
The rest of the paper is organized as follows. LOAF is compared to related work in Section II. In Section III, the problem is formally defined and the considered system model is described. The details of LOAF are provided in Section IV. The validation results are presented in Section V. The paper is finally concluded in Section VI.

II. RELATED WORK
Published techniques for federating the distinct segments or autonomous WSNs can be categorized into two groups [2], [3]: (i) approaches that employ relay nodes and form stable data paths among segments. The main objective of these approaches is usually to minimize the number of populated relays to achieve full connectivity; (ii) approaches that exploit mobility for solving the federation problem. These mobility-assisted techniques opt to create intermittent links. This section discusses related work in these two categories.

A. RELAY NODE PLACEMENT
In general, deterministic placement of relay nodes that are richer in computation, energy and communication resources than sensor nodes, has been pursued as a means for shaping the WSN topology in order to satisfy some desired performance goals. While minimizing the required relay count has been the prime optimization objective, many variants of relay placement have been proposed to achieve additional goals, e.g., degree of connectivity, path length, etc. Achieving connectivity with the least relay count is equivalent to identifying a Steiner minimum tree with minimal Steiner points and bounded edge-length which is shown to be NP-hard by Lin and Xue [4]. Therefore, heuristics have been pursued. Published heuristics can be categorized into three groups.
In the first group, unconstrained setups are considered where the nodes can be virtually placed anywhere in the area of interest. The placement algorithms in this group strive to minimize the relay count needed for restoring connectivity in a partitioned network [5], [8]. In addition to reducing the number of relays, the second group considers more objectives, such as high energy efficiency to prolong network lifetime [9], [10], or high degree of connectivity by providing multiple disjoint inter-node paths in the formed network [11], [14]. Solutions in the third group tackle the federation problem under node position constraints [15], [16] or various quality of services [17], [18]. Overall, the approaches in this category provide perpetual connectivity and do not consider resource-availability constraints. LOAF solves the federation problem when the relay count is insufficient for forming stable data paths and establishes intermittent connectivity instead.

B. MOBILITY-ASSISTED SOLUTIONS
Mobile agents have been employed to transport data in sparse networks by playing a role of a base-station or a data carrier. A mobile base-station moves in the area of interest and gathers data from sensor nodes over multi-hop paths. Meanwhile, a data carrier tours sensors and downloads their readings in one hop to relay or carry them to a sink or another node in the network. Therefore, a mobile data carrier (MDC) eventually forms an intermittently connected topology. Published MDC-based federation schemes fall into one of two categories depending on whether more objectives are considered in addition to establishing connectivity.
The approaches in the first category do not consider a constraint on the availability of the mobile nodes [20]- [23]. For instance, in [20] Almasaeid et al. model the mobile-assisted federation problem as a closed queuing network and focus on the effect of the network parameters related to mobile relays on the end-to-end delay. They expanded their studies in [21] by including two other roles of mobile agents, i.e., mobile sinks and mobile collectors. On the other hand, Li and Hua deploy mobile nodes to form a second-tier mesh network to transfer data from sensor nodes to a sink such that the data delivery latency due to buffer space limitation of the mobile nodes is minimized. Unlike LOAF, the approaches introduced in this group do not consider the limited supply of mobile nodes and thus careful assignment of MDCs is not studied. In addition, Wang et al. [22] and Ma [23] have focused on a single MDC setup and how to limit the length of data paths. However, such work does not deal with segments of nodes and address inter-segments connectivity.
Like LOAF, the second category solves the federation problem with a limited MDC count. IDM-kMDC [24], FeSMoR [25], MINDS [26] and LEEF [27] first find a stable inter-segment topology based on which MDC tours are formed. Basically, an MDC may be dedicated to tour the link between a pair of segments or tour a subset of the segments. In addition, MINDS and LEEF strive to even tour length among MDCs and is compared to LOAF in Section V. Moreover, MiMSI and RCR strive to solve a more constrained version of the problem where only few relays are movable, and the others are stationary [28], [29]. However, unlike LOAF these approaches focus more on tour lengths rather than energy consumed by the MDCs and do not factor in the inter-segment communication latency.
On the other hand, there are some approaches that focus on reducing data delivery latency. I. F. Senturk et al. propose a delay-aware clustering algorithm which groups segments for k MDCs to reduce the maximum tour length among MDCs and data delivery delay between segments to a sink [30]. In addition, FOCUS factors in the data delivery delay in the federation by carefully scheduling the motion of MDCs [31]. It first forms overlapped k clusters served by k MDCs. The intersection segment (IS) of two overlapping clusters plays the role of a rendezvous point. In order to avoid storing data and holding MDCs at the ISs, FOCUS tries to synchronize the arrival of two MDCs by carefully setting their motion speed. However, FOCUS does not care for the data delivery delay and energy concerns.
Meanwhile, ToCS pays more attention to reducing the average and maximum delay for delivering data between segments by finding the balanced tour paths among MDCs [32]. Like LOAF, ToCS groups a set of segments into k clusters that form a star topology in order to reduce the inter-segment latency. Then it opts to equalize the tour length of clusters by adjusting the size of the cluster at the center. However, ToCS does not consider balancing the energy consumption among MDCs during operation. Unlike ToCS, LOAF strives to even the energy overhead for each MDC to tour and transport a distinct volume of data between the terminals which it serves. The consumed energy and the communication delay of LOAF are compared to that of MINDS, LEEF, ToCS, and FOCUS in Section V.

III. PROBLEM STATEMENT
The mobility-assisted federation problem tackled in this paper may arise in two scenarios; (i) restoring lost inter-segment connectivity after a major node damage, e.g., inflicted by explosives in a battlefield or natural calamities such as landslides or avalanches, and (ii) linking individual batches of sensor nodes, for example to enable collaboration among multiple standalone WSNs in order to achieve a common mission such as search-and-rescue, or environment/ creature monitoring. In both scenarios, meeting some intersegment requirements, such as link capacity, may be necessary to achieve the mission; in this paper, we consider the data volume, represented as bits per data collection round, to be transported between every pair of segments. Such an inter-segment requirement can be: (i) just a byproduct of the damage depending on the size of the individual segments, or (ii) required to provide the application service though the federated segments.
The federation is to be achieved using k MDCs that provide intermittent data paths among the segments subject to the data volume requirement. The main optimization objective for such a federation is to determine the MDC tours that reduce inter-segment communication delay and balance the energy overhead experienced by the MDCs while travelling and transporting data. In other words, we employ a set M of k MDCs {M 1 , M 2 , . . . , M k } to connect a set S of n distinct terminals {S 1 , S 2 , . . . S n }, n > 2 which play the role of a gateway node that serves as an interface for the segment. In the rest of the paper the terms terminal and segment are used interchangeably. In LOAF, S is to be clustered into C i 's, i = 1,.., k, i.e., C i ⊂ S and ∀i C i = S. Each cluster C i is served by M i along a travel route TR(M i ) that contains a list of coordinates at which M i stops to upload or download data from/to the terminals in C i . The delay incurred while delivering the inter-segment data between S s to S d denoted as D(S s , S d ) and the energy consumed by M i , E(M i ), could be calculated by (1) and (2), respectively.
In (1), the delay incurred while carrying data from S s to S d is primarily determined by a trip latency D T , a data transmission latency D C , and a relaying latency D R . D T mainly depends on the length of the travel path between two terminals S s and S d , denoted as Trip s,d and the speed of the involved MDCs. We assume a constant speed V M for all MDCs and D T is thus a function of only the tour length of the individual MDC. In addition, D C is determined by the volume of data transfer between S s and S d , and the capability of the radio transceiver (bits per second), represented as Data s,d and B M in (1), respectively. Recall that LOAF forms a star-like inter-cluster topology; thus, inter-cluster relaying may take place. The constant σ captures that fact that the communication delay is incurred more than once since two MDCs will be involved in exchanging the data. The value of σ is set to 1 if S s and S d are in the same cluster, to 2 if either S s or S d belong to the central cluster, and to 3 if S s and S d are part of two distinct outer clusters. The data volume transported between every pair of terminals is assumed to vary based on the size of the corresponding segments.
Lastly, D R means the loading time for inter-cluster data to be relayed from an MDC to another if S s and S d do not belong to the same cluster. In the proposed solution MDCs meet directly to exchange data at a computed position and the inter-cluster data relaying may thus involve the waiting time for rendezvous between MDCs depending on their trip schedule. Therefore, like D C , D R is computed depending on the locations of the communicating segment pair S s and S d . In case S s and S d belong to the same cluster C i , i.e., both segments are served by the same MDC M i , D R becomes zero. Otherwise, the extra rendezvous time may be encountered once or twice depending on which clusters S s and S d belong to as explained above when discussing σ .
Meanwhile, the consumed energy by M i in serving C i , i.e., E(M i ) includes the energy for motion, i.e., E M (M i ), and the ancillary energy for communication, i.e., E C (M i ). In detail, E M (M i ) represents the consumed energy during M i motion while it tours the segments of C i once. In addition, E C (M i ) includes the required energy for M i to upload/download two types of data traffic: the intra-cluster data in C i and inter-cluster data, i.e., data imported from or exported to another cluster C j . Therefore, E M predominantly scales with a trip distance of M i serving C i , i.e., TR(M i ) in meters while E C is dependent on the volume of data, Data M i , uploaded/downloaded over a wireless link, i.e.,

Data S x , S y
We assume using an energy cost model for E M that is proportional to the distance, as seen in (3), while E C is primarily proportional to the power for transmitting a single bit over a wireless link seen in (4).
In (3), µ ranges from 0.1 to 1 J/m [33]. In addition, the energy required to transmit 1 bit is 2 · 10 −6 Joule, where α = 100nJ, β = 0.1nJ/m ∂ , ∂ = 2 in (4) [34]. During the federation, LOAF strives to balance E(M i )'s, ∀i by factoring in the motion and communication related energy overhead, i.e., E M (M i ) and E C (M i ) respectively. Overall, the problem that we tackle in this paper is captured mathematically by the following formula: where ∀i C i = S such thatD(S p , S q ) and The problem presented in formula (5) is to find a set of clusters C i 's that covers S, each of which includes a set of terminals that an MDC M i visits such that the inter-terminal data delivery delay is reduced and energy overhead for the individual MDCs is balanced. In addition, we suppose that all MDCs have the same capabilities with enough data storage to handle the inter-segment data traffic in each cluster, i.e., we do not consider any buffering constraints in our solution. Without considering any additional objectives, the formulated problem can be mapped into solving a k-means clustering problem that is known NP-hard [4], and thus LOAF pursues heuristics.
A sensor does not need to have a global map of the area. The network is modeled at the level of segments rather than the level of sensors. Discovering segments can be done by land-based robots or UAVs. Once the segment locations are known, the area is mapped into a grid and the segment cells are identified, as explained in detail in the next section. LOAF could be executed at a centralized command center or by one of the MDCs and then the tours are communicated to the individual MDCs. An MDC is assumed to have sufficient buffer space for the data transported in one tour. Additionally, the paper focuses on the algorithmic aspect of the inter-networking problem without considering diversity of the physical, link and network layers. It is also assumed that all MDCs have the same communication range R which is equal to that of a sensor r, i.e., R = r. This is a simplifying assumption to ease the presentation. In addition, coverage is not the focus of LOAF although MDCs may have sensing capabilities that can mitigate coverage loss caused by the damage during their tours. Finally, we assume that the data volume generated by sensors, i.e. sampling rate, is fixed and determined by various application-specific missions [38], [39]; thus the communication load between segments stays constant during network operation. Nonetheless, we study the effect of variation in the data volume in Section V.

IV. THE LOAF APPROACH
To provide energy balanced federation of the n terminals using k MDCs, LOAF groups the terminals into a set of k clusters in a star inter-cluster topology, where a centralcluster C k serves for data relaying between pairs of clusters. In the first phase, LOAF computes eG, i.e., an energy-based center of mass, of a set of segments S based on the inter-segment related communication energy which is proportional to traffic volume exchanged between segments. Then it strives to form non-central-clusters C i 's i<k around eG while minimizing the overall energy consumption in the clusters in terms of motion. In the second phase, LOAF opts to form a central cluster around eG while balancing energy among C i 's, ∀i. The details of LOAF are provided in the balance of this section.
A. 1st PHASE: FORMING NON-CENTRAL CLUSTERS CONSIDERING HETEROGENEOUS INTER-SEGMENT DATA VOLUME LOAF first tries to find the center of mass eG of S considering energy consumption required for the inter-segment VOLUME 8, 2020 FIGURE 1. In (a) the number on an edge represents data volume exchanged between two segments in megabits. In order to intermittently connect 12 segments by k MDCs, LOAF first computes the weighted core of mass eG of 12 segments with regards to the energy consumption considering inter-segment data volume. The numbers written in each circle shown in (b) represent the aggregated amount of inter-segment data traffic involved to each segment and eG is thus determined towards the circles which have larger numbers. data transportation. Then non-central clusters, C i 's i < k are formed around the found eG while minimizing energy experienced while MDCs travel the formed non-central clusters. The details of the first phase are provided below.

1) COMPUTING AN ENERGY-CONSIDERED CORE OF MASS
Prior to grouping segments into clusters, LOAF first tries to find the appropriate location for a central-cluster C k via which the inter-segment data traffic between clusters is forwarded in a star-shaped cluster topology. Since the objective of LOAF is to balance energy consumed by MDCs that serve clusters, the ideal location of the central cluster ought to be at the center of groups of segments with respect to energy consumption of the MDCs, i.e., a sum of E M (M i ) and E C (M i ) each of which is mainly affected by data traffic volume between segments and the inter-segment proximity, respectively. In other words, LOAF finds the center of mass of segments i.e., eG, considering data volume as well as proximity.
Therefore, for computing eG(c x , c y ) LOAF first calculates the total data volume coupled with each segment S i , i.e., a sum of traffic originated from/destined to S i which is hereafter denoted as Data S i that is equal to Then the x-and y-coordinates, c x and c y are calculated in the same way to find a center of mass of the weighted vertices. In other words, c x and c y equal , respectively, where x(S i ) and y(S i ) represents x-and y-coordinate of a segment S i . Figure 1-(b) shows the found eG assuming the area of interest is 270 × 360m 2 and the cell width is corresponding to R √ 2 , R = 30m. The eG is located in a different position from the centroid G computed only considering locations of segments. In the figure, the number in a circle of S i represents Data S i in megabits based on the numbers on an edge e(S i , S j ) that means the volume of data that is exchanged between S i and S j i = j in Figure 1-(a). In consideration of Data S i 's, the location of eG moves towards the position where the heavy data exchange overhead is involved like around S 3 .

2) FORMING NON-CENTRAL CLUSTERS
For federating the segments S i ∀i ∈ S with k MDCs in an energy balanced manner, LOAF tries to group the S i 's in a star inter-cluster topology, where each cluster is served by a distinct MDC and the inter-segment data delivery can be operated within at most two cluster hops. Then, LOAF tries to equalize the energy overhead of MDCs in adjacent clusters. In order to reduce the overall energy consumed in the clusters by the MDCs, LOAF opts to group segments to minimize energy overhead experienced by each MDC serving C i , i < k. Therefore, the segments are grouped into (k − 1) non-central clusters in rounds during which LOAF strives to reduce the sum of E (M i ) ∀i, i.e., ∀i E(M i ) in each round. Initially we assume that a central cluster C k is formed by placing an MDC M k at eG as a stationary relay and includes the segments within a radio range of M k that is R, i.e., In the first round (r = 0), for each is an Euclidean distance between a and b. Obviously, it is sufficient for an MDC to be at a distance R from the segments and from M k in order to establish communication links, assuming free space signal propagation model. In the second round (r = 1), LOAF opts to combine two clusters C x and C y whose merging leads to the greatest decrease in the overall tour length. This step is performed repetitively. Thus, the number of clusters in round r denoted as N cluster decreases by one in each round. In other words, a pair of C x and C y which satisfies the equation (6) is selected in each round r ≥1.
In (6), ME(C x ∪ C y ) represents energy required for an MDC to serve the merged cluster that includes C x and C y for transporting data and travelling. E C C x ∪ C y is mainly affected by the aggregated data volume, i.e., Data S x + Data S y and E M C x ∪ C y , the updated trip that is the shortest path in the merged cluster C z . Since the goal of this step is to group segments in the form which minimizes ∀i E M (M i ) and ∀i E C (M i ) and ∀i E C (M i ) is already determined by given data transport requirements between segments, LOAF focuses on reducing ∀i E M (M i ) in the clustering process. Therefore, a pair of C x and C y whose merged tour path decreases ∀i E M (M i ), will be selected. Computing such a merged path of C x and C y is equivalent to the problem which finds the shortest Hamiltonian cycle to visit S i s∀i ∈ (C x ∪C y ) considering R that is NP-hard. Therefore, LOAF uses the heuristic solution in [24], [35], [36] to compute a tour path of C z . The clustering procedure is repeated until N cluster become (k − 1) and the 2 nd step of the first phase thus terminates as r=N 0 cluster − (k − 1). We refer to the point P i on the circle of radius R and centered at eG, where M k is placed, as the rendezvous points between M i i < k and M k . When reaching P i , M i will be able to establish communication with M k and exchange relevant data payload. The position of rendezvous points will be adjusted in the 2 nd phase of LOAF as we explain in the next subsection. Figure 2 shows the formation of non-central clusters using the example seen in Figure 1 as k = 5. We assume that R is 30m and the required energy to move along TR(M i ) is computed according to equation (3), where µ = 1 J/m. In addition, 2 Joules are required to transmit 1 megabit over wireless communication according to (4). For these settings, Figure 2 shows that the twelve segments are grouped into C i , i= 1, 2, 3, 4, in 8 rounds. In the 1 st rounds (r = 0), M 5 is to be placed at eG where S 3 happens to locate and forms While in the 1 st phase LOAF focuses on reducing the overall energy overhead experienced by M i , i < k in touring noncentral clustering, the major objective of the 2 nd phase is to equalize energy overhead for all MDCs. Since a central cluster C k is initially formed by placing M k at eG as a stationary relay in the 1 st phase, we adjust the size of C k for energy balance during the 2 nd phase. In other words, the star inter-cluster topology centered at C k is re-formed by moving P i outwards or inwards depending on the relative energy consumption of M i . This phase consists of two steps. In the first step, C k is grown by shirking the non-central clusters whose MDCs consume more energy than the average among all MDCs, denoted as E AVG . In other words, the rendezvous point, P j is moved outwards from eG for a non-central cluster C j whose designated MDC, M j , consumes more than E AVG . The step is iterative since the tour length of re-formed clusters will change and subsequently E AVG . The 1 st step terminates as M k consumes energy more than E AVG . Then, the second step is geared to adjust the size of non-central clusters whose MDCs consume less than E AVG , VOLUME 8, 2020 where the rendezvous points for these clusters are moved inwards toward eG. Both steps are iterative in nature and are performed in rounds. The following notation used in the discussion.
• C r i : reflects the segments grouped into a cluster C i in round r. C 0 k includes segments that are reachable from M k which is placed at eG i.e., {S i |EuclideanDist(S i , eCoM ) ≤ R} and C 0 i 's, i < k are the same as the 1st phase.
• P r i : It represents a rendezvous point where M i i < k meets M k in round r. P r i 's ∀i are always on the straight line between eG and CoM r−1 i which will be explained later.
• TR r i : The travel path that M i takes in round r while visiting the segments in C i is denoted as TR r i . It is equivalent to the shortest path where M i departs from P r i and visits every segment S i ∈ C i once and returns to P r i . Since finding TR r i is mapped into the Travelling Salesman Problem, the heuristic solution of [24], [35], [12] will be used to find TR r i . • CoM r i : It represents a core of mass of the polygon formed by the segments of C i and P r i in round r. In round r of the 2nd phase of LOAF, C k may be expanded by moving P r i towards CoM r−1 i of C i or C j may be extended by relocating its P r j towards CoM r−1 k . • E r i : denotes the energy experienced by M i in round r for up/downloading intra-cluster data in C i and inter-cluster data at P r i i.e., E C (M i ) and also during completing one  (3) and (4), respectively.
• E r AVG : equals an average value of E r i ∀i. With the provided notations, the 2 nd phase of LOAF opts to balance the energy overhead by adjusting the MDC tours. Basically, LOAF tries to adjust rendezvous points P i 's of C i 's outwards or inwards based on the average energy overhead. In other words, LOAF relocates P m outwards towards C m if E m > E AVG in order to reduce the heavy energy overhead of C m or reposition P l inwards towards eG, where C k is initially formed if E l < E AVG for expanding C l . Since the computed eG during the 1 st phase lies inside the convex hull of the segments, as will be proven in Lemma 1, and the initial energy overhead E 0 k of forming C k at the eG, is less than E AVG , as will be proven in Lemma 2, (i) the rendezvous points P m 's for C m 's whose E r m > E r AVG are moved outward while E r k < E r AVG and then (ii) P l 's for C l 's whose E r l < E r AVG are also handled while E r k > E r AVG . Each of the steps (i) and (ii) is repeated in rounds until there is no more improvement of the standard deviation (SD) of E i ∀i as explained below.
(i) moving P i s outwards: During this step, LOAF iteratively shrinks the boundary of clusters, C m 's, of heavily loaded MDCs, and accordingly expands C k . In the first round (r = 0), for each cluster C i , i = 1, . . . , k − 1, P 0 i , TR 0 i , and reflects only E C (M 5 ) which includes energy consumption for transporting the inter-cluster data traffic volume represented using double dotted lines in Figure 3. Therefore, E C (M k ) increases when high volume of data traffic is delivered between clusters. LOAF relocates P i 's away from eG starting with clusters whose MDCs consume energy more than average and adjusts their tour accordingly. For the relocation of P i 's, LOAF first determines the relative movement rate ϕ i of each P i based on the energy imbalance among the MDCs, i.e., j . In other words, ϕ i factors in the relative excessive energy overhead of each M i to the least energy consuming MDC. In order to adjust the actual moving distance in meters, a constant parameter, ε (≥ 1) is multiplied to ϕ i . With excessively large values of ε, the convergence to form the energy-balanced clusters may be fluctuated while small ε slows the convergence of energy balancing. Thus, an appropriate value of ε, should be selected. Since the formed clusters are served by MDCs, the communication range of an MDC, i.e., R is the recommended setting for ε in practice.
Based on ϕ i and ε, LOAF expands a size of C k and accordingly reduces that of C i by moving P i away (ϕ i × ε) meters along a line from P i to a core of mass of a polygon formed by segments grouped to C i in round r = 0 denoted as CoM 0 i . After that tour paths of M k and M i , i.e., TR k and TR i , are recomputed using an updated rendezvous point P i . Accordingly, E k , E i and CoM i are also updated. In addition, re-grouping of segments may occur, e.g., S x ∈ C i may be included to C k if S x becomes reachable from M k after expanding C k . Grouping all segments to k clusters is maintained during this process as will be proven in Theorem 1. The same process of C k expansion is repeated in successive rounds and terminates in round f where M k consumes energy more than average, i.e., E k ≥ E AVG . Therefore, the process is converged in O ( Dist(eG,L) ε ), where L is the smallest polygon that includes all segments, and Dist(eG, L) represents a distance from eG to the furthest point on L.
(ii) moving P l inwards: This step adjusts P l 's of C l 's, whose serving M l requires less energy than average, i.e., E l < E AVG . Thus LOAF tries to extend the size of C l 's by moving the P l 's towards C k , exactly towards eG or a core of mass of C k , i.e., CoM k in case C k includes more than one segment. Accordingly, TR k is shortened. For repositioning of P l 's, LOAF also computes ϕ l which reflects the relative energy shortage of M l to the least energy consuming MDC and is found in the opposite way of computing ϕ i , i.e., ϕ l = E least E l and then P l moves inwards (ϕ l × ε) meters along a line from P l to CoM k . Using ϕ l , the less energy overhead M l incurs, the more distance P l moves inwards towards CoM k . Thus C l is accordingly extended and E l also increases. After that, TR l , CoM k , and E l , E k and E AVG are updated. The same procedure is repeated until E k ≤ E AVG . Figure 4 shows the procedure of the 2 nd phase of LOAF as ε is equal to R. In the first round (r = 0) of the C k extension step, the initial rendezvous points P 0 i 's ∀i < k are located at eG. Then each C i relocates ( × R) meters, i = 2,3,4 respectively towards CoM 0 i i= 2, 3, 4 as seen in Figure 4-(b). This is because M 0 2 , M 0 3 , and M 0 4 consume more energy than E 0 AVG . Accordingly, C 1 5 is extended towards C 0 2 , C 0 3 , and C 0 4 as seen in Figure 4-(c). In addition, the same process is applied to C 0 2 , and C 0 3 in a subsequent round as shown in Figure 4-(d). After that S 10 becomes unreachable to M 2 , and accessible to M 5 ; therefore, S 10 changes association to C 5 . Figure 4-(e) to (h) show the 2 nd step. The first round of that step, C 0 1 , C 0 3 , and C 0 4 grow towards C 5 by adjusting their rendezvous points. Similarly, C 0 1 , and C 0 4 are extended in the second round. Finally, the resulting intermittent topology of k (= 5) MDCs formed in an energy-balanced manner for federating twelve segments after the first round of the 2 nd phase is presented in Figure 4-(i). The pseudo code of the 2 nd phase of LOAF is described in Algorithm II. Lines 9-12 describe the first step and lines 23-32 explain the second step. As a result, LOAF returns k sets of segments each of which is served by an individual MDC and their tour paths, i.e., {C i , TR i ∀i } in line 33.

C. ALGORITHM ANALYSIS
LOAF is analyzed in this subsection. We mainly focus on proving that the energy imbalance among MDCs is minimized by LOAF while forming a star inter-cluster topology. In addition, the complexity of LOAF is analyzed to show that the resulting cluster topology is formed within an execution time bound. We introduce the following theorems and lemmas: VOLUME 8, 2020 FIGURE 4. The 2 nd phase of LOAF is dedicated to balance energy among MDCs by adjusting the rendezvous points P i , i < k. Balancing is performed in an iterative manner during which LOAF expands C k by moving P i outwards towards C i if E i > E AVG in order to reduce more-than-energy consuming clusters C i 's,(a)-(e) and then P l 's of C l 's whose E l <E AVG are moved inwards towards C k , (f)-(h). (i) shows the result of the two steps.

Lemma 1: In case that N seg is more than two, the energybased center of mass among segments during the 1 st phase of LOAF, denoted as eG, always lies inside the convex hull of all segments.
Proof: The computed energy-based center of mass among segments, denoted as eG can be one of three cases [40], [41].
(1) If there are only two segments, i.e., N seg = 2, then eG lies on the line connecting the two segments. (2) If N seg ≥ 3 and the segments form a convex polygon as illustrated by the example in Figure 2, then eG lies inside the polygon. (3) If N seg ≥ 4 and the segments form a concave polygon as an example seen in Figure 5, then eG may lie outside the polygon depending on the inter-segment data volume as seen in Figure 5-(a). However, the eG lies inside the convex hull which includes all segments, represented as a solid polygon in Figure 5-(b). In addition, Figure 5-(c) shows the resulting topology formed by LOAF. Therefore, the computed eG in the 1 st phase of LOAF always lies inside the convex hull of the segments.
Lemma 2: The energy consumption of M k serving for the central cluster formed in the 1 st phase of LOAF is larger than the average energy of all MDCs, i.e., E o k > E 0 AVG . Proof: Via the 1 st phase of LOAF, the initial inter-cluster topology is formed in a star shape, where a central cluster C k is formed by placing M k as a stationary relay at the computed eG, around which (k − 1) non-central clusters are formed. Segments residing within R from M k are made part of C k and the rest of segments are grouped into C i , i < k. Therefore, the energy consumed by M k , E o k is completely determined by E C (M i ), which is primarily affected by the sum of all inter-segment data volume, i.e., E o k ≈ ∀i,j,i =j Data(S i , S j ). In addition, the average energy consumption of all MDCs, Proof: The 1 st phase of LOAF is devoted to forming (k −1) non-central clusters, during which at most N seg of clusters are grouped into (k − 1) clusters via successive merging two clusters in subsequent rounds. The maximum number of non-central clusters corresponds to the first round (r = 0) and equals (N 0 cluster − k + 1), where N 0 cluster ≤ N seg . The main time complexity of each round comes from finding a tour path of each cluster, i.e., TR(M i ), which is computed using the heuristic whose execution time bounds to O(n 4 logn) [24], where n is the number of segments in a cluster in our case, i.e., 1, 2, 3, . . . , (N 0 cluster − k + 1) each round. Thus the 1 st phase's time complexity equals Theorem 1: LOAF guarantees the convergence to grouping N seg segments into k-clusters in a star topology.
Proof: As proven in Lemma 3, LOAF groups N seg segments into k-clusters in its first phase. Thus, for the proof of the convergence of N seg segments into k-clusters, it is sufficient to show that (i) a segment S i which is not visited by the updated tour of M i is necessarily visited by M k during the first step of the 2 nd phase, and (ii) vice versa, for S i that is not visited by TR r k ought to be covered by TR r i , ∃i < k during the second step.
For proving (i), it is required to show that a candidate S i for re-clustering is always placed between a convex hull CH r of {S j ∀j ∈ C i , P r i } and TR r i which is R away from CH r and will be visited by M i or M k in the next round (r +1). It is proven by contradiction. If S i resides outside CH r or inside R away from TR r i , it self-proves the found CH r or TR r i is incorrect due to the natural features of a convex hull and the way of computing a tour path described in [24] respectively. Therefore, S i that will be re-grouped into C k is undoubtedly inside CH r and in a range R from TR r i . In addition, in the cases in which S i will not be reachable from TR r+1 k and thus not be re-clustered into C k as seen in Figure 6-(c) and (d), the S i will be necessarily visited by the updated tour path TR r+1 i as Figure 6-(a) and (b) show. The same proof applies to (ii) and thus k-clustering of the segments formed in a star topology is guaranteed by LOAF.
Theorem 2: The time complexity of LOAF is proportional to the computation time for TR r i which is determined by a gap between N seg and the number of the available MDCs (k), as ((N seg + N r k) · (N seg − k) 4 · log(N seg − k)), where N r is the maximum iteration of the 2 nd phase and bounds to O( Dist(eG,L) ε ), k is the number of available MDCs and N seg is the number of segments in the area L.
Proof: As proven in lemma 3 the 1 st phase of LOAF is bound to O((N seg −k)·(N seg − k) 4 log (N seg − k)). In addition, the 2 nd phase of LOAF is iterative in two steps. The number VOLUME 8, 2020 , where L is the smallest polygon that includes all segments, and Dist(eG, L) represents a distance from eG to the furthest point on L in meters. In addition, the execution time of each round in both steps is determined by computing TR(M i ) for at most (k − 1) clusters and the average number of elements in clusters tentatively formed during the 2 nd phase is N seg k . In addition, the two steps are iterative while the standard deviation of E i , ∀i has been improved. Therefore, the 2 nd phase of LOAF requires the execution time complexity which is bounded by (N r k · ( N seg k ) 4 · log( N seg k )). In conclusion, the time complexity of LOAF for grouping N seg segments into k-clusters in an energy-balanced manner equals {(N seg − k) ·

V. PERFORMANCE EVALUATION
In this section, the effectiveness of LOAF is validated through simulation. The simulation experiments study the performance with respect to the number of RNs populated by LOAF in comparison with the best known and recently published algorithms. The quality of the resulting topology of LOAF is also discussed.

A. SIMULATION ENVIRONMENT AND PERFORMANCE METRICS
We have implemented a simulation environment in C. The environment articulates the effect of damage on a single WSN that originally covers an area or multiple autonomous WSNs. Basically, varying numbers of segments are randomly located in an area of interest 1200m×1200m such that the segments are evenly distributed in the quadrants. The following parameters are used to vary the network characteristics: • Communication range of relays (R): In general, R has the influence on forming clusters which include a set of segments visited by an MDC. The length of tour path is also affected by R, specifically, MDCs need to travel a shorter path with a larger R.
• Number of segments (N seg ): Having high segment count may increase the connectivity requirement and thus more energy may be needed for MDCs because of the longer tour. In addition, involving more segments may increase the traffic volume where more data is exchanged among segments and thus inter-MDC energy balancing becomes more complicated.
• Number of MDCs (N MDC ): The given number of MDCs is assumed to be less than the least count of the required relay nodes to form a perpetual topology of N seg segments, denoted as N RN . We use the algorithm in [7] to compute N RN which primarily depends on N seg and the layout of segments. In the simulation, N MDC is determined based on N RN as explained in subsection C below. As the value of N MDC gets reduced, MDCs may consume more energy for visiting more segments.
• Average Inter-Segment Data Volume (ISDV ): It represents the data traffic requirements between each pair of segments. The value of ISDV would have influence on energy consumption of MDCs for wireless communication and the inter-MDC energy balancing.
The performance of LOAF is assessed using the following four metrics: • Maximum inter-segment communication delay (D max ): Obviously, LOAF strives to minimize the maximum data delivery latency between segments. D max is mainly determined by rendezvous time along the path between two furthest apart segments, which is affected by a count of clusters and inter-segment data traffic volume.
• Energy balance among MDCs: This is also a main objective of LOAF. Since LOAF tries to balance energy considering motion and communication both, energy balance among MDCs is computed as a standard deviation of total energy consumption of each MDC for motion and communication, i.e., it equals • Average energy consumption of all MDCs (AEC): It measures the average energy consumed by all MDCs before the first MDC dies. It will represent the absolute amount of energy consumption of MDCs for intermittently connecting segments.
• Network lifetime (NL): This indicates how long the formed intermittent topology stays fully operational and is measured as the duration until the first MDC fully depletes its on-board energy supply. In other words, NL represents the length of time during which every MDC operates and serves their clusters. This metric indicates the maximum energy consumed by an MDC. We measure NL as (initE−AEC)

BPC
, where initE is the initial energy of an MDC, BPC is battery power consumption of an MDC per second.
• Buffer space required at gateway segments: This metric is relevant to only the case in which some MDCs share a segment in their tours and uploads/downloads inter-cluster data from/at the buffer of the common segment. The maximum buffer space required within a certain time window is measured.

B. BASELINE APPROACHES
The performance of LOAF is compared to four competing approaches. The first two solutions focus on reducing inter-segment communication delay. One of them, namely ToCS [32], forms clusters of segments in a star topology like LOAF and balance tours of MDCs. The second is FOCUS [31], which opts to reduce the tour lengths of MDCs and adjusts their speed to minimize the travel distance and time required for transferring inter-clustering data between MDCs. Meanwhile, the focus of the third baseline approach, namely, MINDS [26], is more on reducing and balancing the MDC tours than reducing data delivery delay between segments. Like LOAF, the fourth approach is LEEF [27], opts to achieve MDCs' energy balance and optimize inter-segment delivery latency. These baseline approaches address the same problem tackled by LOAF using different solution strategies, as summarized below.
• ToCS forms clusters around the center of the area G and consists of two phases [32]. In the first phase, each cluster segment initially becomes a cluster C i , and then combines two C i 's whose merging cost based on G is the least. The merging is repeated until (k − 1) clusters are formed. Then a center-cluster C k is formed by including (k − 1) rendezvous points P i , i = 1,..,(k − 1), each of which is computed as a mid-point between G and the closest point ''x to G that is on the convex hull of segments of C i . Then each tour path is determined as done in IDM-kMDC [24] and the average tour length TL avg is found. ToCS then adjusts the size of C k towards C i in order to balance the MDC tour lengths in the 2 nd phase. During the 2 nd phase, C k expands towards C i whose tour length TL i is larger than TL avg by moving P i along the line between G and x of C i until TL i > TL avg . In the case of TL i < TL avg P i moves towards G. The same process is repeated for each C i ∀i and the 2 nd phase terminates when TL avg ≈ TL i , ∀i. In ToCS the waiting time at the rendezvous point contributes to the inter-segment communication delay due to the need for MDC synchronization where data uploading/downloading is performed.
• FOCUS operates in three phases [31]. In the 1 st phase, segments are grouped into k disjoint clusters based on proximity. Each cluster is to be served by an MDC. In order to minimize the tour path of an MDC, clustering is initiated by selecting k farthest away segments from the centroid and then the remaining segments are joined in a greedy way. The set of k disjoint clusters is represented as a directed graph G = (V , E), where V reflects clusters and E contains a set of weighted directed edges −−−→ C a , C b between every pair of clusters. The weight of −−−→ C a , C b is equal to the increase in the tour length of C a when C a is extended towards C b by including a segment from C b . During the 2 nd phase FOCUS opts to overlap the k clusters in order to minimize tour lengths of MDCs for the inter-cluster communication; it does so by selecting an intersection segment (IS) between two adjacent clusters C a and C b . The pair of C a and C b corresponds to two end vertices in each edge of the computed minimum spanning tree (mst) of G. In the 3 rd phase, FOCUS adjusts the motion speed of MDCs for reducing the time required at IS for the data communication between clusters.
• MINDS strives to balance tour lengths among k MDCs and consists of three phases. In the 1 st phase, it calculates an mst of segments. If only one MDC is available, the MDC tours the segments along the mst edges. Otherwise, MINDS opts to split the longest tour L into two groups until the number of groups equals k in the 2 nd phase. Spitting is done by finding a center segment V c of L from which the path on mst to the furthest segment is shortest. Then, the segments in L are divided into two groups g a and g b and V c is designated as a rendezvous point between MDC a and MDC b . Forming g a and g b is based on the node degree of V c . If there are more than two edges connected to V c , then grouping takes three steps. First g a is formed by the segments connected through the edge along which the furthest segment is reached from V c . Then the remaining segments are grouped into g b in the same way. If there are still ungrouped segments, each of them belongs to the closest group between g a and g b . In the 3 rd phase, the tour path of MDCs is computed as done in [24].
• LEEF groups the segments into a set of k clusters in a star topology where a hub-cluster C k facilitates data relaying between clusters. In the first phase, LEEF models an area of interest as a grid of equal-size square-shaped cells, based on which a set CS T of the fewest cells that cover all segments is identified by evaluating each cell's reachability to segments, and proximity to the center G of the area. Then LEEF groups the cells in CS T into k VCs considering inter-cell proximity. In the second phase, LEEF opts to use the VCs to guide the formation of energy balanced k-clusters in a greedy manner through a two-step process: greedy-expansion and optimization. During greedy-expansion, LEEF operates in rounds. Starting with C k = VC k and C i = {G, the closest cell to G ∈ VC i }, in each round r energy overhead of C i , denoted as E r i , is computed based on the intraand inter-cluster data up/download and the MDC tours between the involved segments in C i up to round r. Then, the least energy consumed cluster C least is selected for expansion by adding a segment. In the optimization step, balancing inter-cluster energy is performed by adjusting cluster membership to enable C least to grow. Overall, the four baseline approaches all try to minimize tour lengths of MDCs. Like LOAF, LEEF and ToCS form a star inter-cluster topology while FOCUS and MINDS establish a cluster-based mst. Also, in FOCUS, MINDS, and LEEF, the MDCs rendezvous via a common segment for transferring inter-cluster traffic while in ToCS MDCs meet at a point where no segment is located. In order to minimize the waiting time for rendezvous ToCS strives to even MDC tours.
However, ToCS does not schedule MDCs' rendezvous time. FOCUS also strives to reduce buffering space and time consumed at the common segment by adjusting the motion speed of MDCs. However, ToCS, FOCUS, and MINDS do not consider energy issues like LEEF and LOAF.

C. SIMULATION RESULTS
We have simulated multiple configurations, each has different combinations of values R, N seg , N MDC , and ISDV a . The value of R is varied from 50 to 250 with increment of 25 and N seg takes the values between 21 and 39 with increment of 3. In addition, the data volume between segments is randomly picked using a Gaussian distribution with mean, that takes values from {1, 2,4,8,16,32, and 64} with a standard deviation of 3. The other parameters for simulation setup are summarized in Table 1. We note that the value for Speed MDC is based on nominal speeds of search-and-rescue robots, e.g., iRobot PackBot 510 [36] whose maximum speed is 9.6 km/h, i.e., about 2.59 meter/s. The results of the individual experiments are averaged over 30 runs and all results thus stay within 10% of the sample mean due to 90% confidence interval analysis.  Figure 7 shows that LOAF experiences less worst-case intersegment data transfer latency than all baseline approaches in terms of R, N seg , N MDC and ISDV a . D max is mainly affected by rendezvous time along the path between the furthest apart segments; Therefore, D max is affected by a count of clusters in the path and inter-segment data volume and not much dependent on R. However, as seen in Figure 7-(a), MINDS, FOCUS, LEEF and LOAF show less D max with larger R. This is because R has influence on the inter-cluster path length and traffic volume in their algorithms. In other words, in MINDS and FOCUS the inter-cluster traffic is delivered via a segment overlapped by multiple clusters and larger R makes a smaller number of cluster hops between two furthest apart segments.
In addition, both LEEF and LOAF ensure that there are at most two hops between any pair of segments and unlike ToCS which also forms a star topology, they consider energy affected by R during clustering. Nonetheless, LOAF yields the least D max among all approaches, which is attributed to the following four design features: (i) forming a star-shaped inter-cluster topology where the number of clusters between every pair of segments becomes at most three (like ToCS and LEEF, and unlike FOCUS and MINDS); (ii) MDCs in LOAF do not need to pause and wait for exchanging data between clusters during their travel and thus no extra time for rendezvous is needed in the data delivery (like LEEF, unlike ToCS); (iii) LOAF tries to keep a pair of segments which exchange large volumes of data in the same cluster by considering the inter-segment data exchange overhead during cluster formation. This reduces the inter-cluster traffic volume. While the latter feature is also supported by LEEF, LOAF distinguishes itself by forming a more efficient inter-segment topology, particularly in designating the central cluster. LOAF first locates the central cluster at the energy-balanced center of mass among all segments in terms of communication and motion; then non-central clusters are formed considering segments' individual position. Meanwhile, LEEF identifies the central cluster after forming the non-central ones. Accordingly, the inter-cluster topology formed by LOAF better factors in inter-segment data volume and proximity and thus yields less inter-segment data exchange latency. It is worth noting that ToCS which also forms a star inter-cluster topology has the largest D max with all values of R. This is because ToCS does not reduce rendezvous time by careful scheduling of the MDC tours.
Moreover, as seen in Figure 7-(b) D max grows for all approaches when the number of segments, N seg increases. Such a growth is intuitive since adding more segments not only requires longer trips of MDCs but also involves heavier inter-segment data traffic, and subsequently more stops and longer loading time. Nonetheless, LOAF and LEEF yield lower latency than all baselines regardless of N seg . This is because they strive to include a pair of segments which exchange data in the same cluster, and hence reduces intercluster trip for data transfer and diminishes inter-segment data delivery latency. In addition, LOAF outperforms LEEF, which is again attributed to how LOAF places the central cluster that plays the role of a hub for the inter-segment communication. It is worth noting that the performance of ToCS is worse than FOCUS and MIND due to the implicit waiting time for MDC rendezvous to support data up/downloading.
In addition, LOAF yields less D max than all baselines for various numbers of MDCs as seen in Figure 7-(c). Such performance is due to the advantage of forming a star inter-cluster topology, in which data delivery between any pair of two segments requires at most two MDC rendezvous. Although both LEEF and ToCS also form a star topology, ToCS involves waiting time during MDC rendezvous and LEEF pursues inferior clustering procedure as mentioned earlier. It is worth to note that ToCS and LOAF experience little changes in D max when varying N MDC , while D max slightly decreases as N MDC grows. This is because ToCS, LOAF and LEEF form a star topology where D max is mainly affected by a tour length in a central cluster. Unlike ToCS and LOAF which strive to equalize the tour length for all MDCs, LEEF initially forms a central cluster by placing an MDC at a geographical center of an area and (N MDC − 1) of virtual non-central clusters which are merged. Thus, a larger value of N MDC tends to shorten a tour length in a central cluster of LEEF. Meanwhile, increasing N MDC raises D max in MINDS and FOCUS since they form a mst-based topology of clusters where the more MDCs are involved, the higher inter-cluster communication traffic along the path between two the furthest apart segments becomes and consequently D max increases.
As seen in Figure 7-(d), growing the inter-segment data volume boosts D max . This is fairly anticipated because increasing the data exchange between segments implies that the MDCs take more time in data up/downloading. However, it is worth noting that D max for LEEF and LOAF is much less than its value in ToCS, FOCUS and MINDS. For instance, with ISDV of 64Mb LEEF and LOAF yield 9% of D max of ToCS and 12% of D max of FOCUS. In addition, as ISDV grows, D max increases at a much lower rate in LEEF and LOAF than the other three approaches. These results are due to the fact that LEEF and LOAF factor data volume between segments in determining the cluster membership. Meanwhile, ToCS, FOCUS and MINDS do not consider data traffic volume between segments during clustering.

2) ENERGY BALANCE AMONG MDCs
In Figure 8, the effectiveness of LOAF in terms of energy balance among MDCs is validated. LOAF yields better performance than all baselines regardless of R, N seg , N MDC and ISDV since it: (i) considers energy consumed by MDCs in up/downloading inter-segment data traffic, and in touring between clusters, and (ii) strives to equalize the energy overhead while forming the inter-cluster topology. Moreover, LOAF's optimized design enables it to outperform LEEF which also considers energy balancing during cluster formation. In other words, unlike LEEF which locates the central cluster geographically at the center of the deployment area, LOAF forms the central cluster to reduce the energy overhead. In addition, LOAF considers locations of individual segments and thus optimizes the formation of balanced clusters using more precise computation than LEEF.
As seen in Figure 8-(a), balancing the energy overhead among MDCs has nothing to do with R for all approaches. Meanwhile, all approaches show more balanced clustering topology with smaller N seg as shown in Figure 8-(b). This phenomenon is because an MDC consumes its power for up/downloading data traffic volume exchanged between segments as well as touring the segments. Thus, equalizing energy consumption among MDCs gets highly complicated when more segments are involved and subsequently the combinations of inter-segment data volume vary. This is especially evident in FOCUS, MINDS and ToCS, all of which do not consider energy used for the inter-segment data exchanges during clustering and thus the inter-MDC energy balancing rapidly drops with large N seg . Meanwhile, LOAF outperforms all baselines for various values of N seg and its superiority scales with N seg . Moreover, Figure 8-(c) demonstrates that the star intercluster topology formed by LOAF, LEEF and ToCS has more positive impact on load balancing as N MDC grows than that of the mst-based topology formed by FOCUS and MINDS. Formation of clusters around a central cluster provides higher flexibility in adjusting proximity and traffic volume between clusters than a mst-based topology; such increased flexibility becomes even more influential as N MDC increases. Finally, Figure 8-(d) demonstrates how LOAF efficiently copes with the increased inter-segment data volume and thus it outperforms all baselines in terms of energy consumption balance. This result comes from the fact that LOAF tries to keep a high volume of data exchanging segments in the same clusters and the positive impact of the design principle becomes clearer as the inter-segment data volume, ISDV grows. Figure 9 reports the average energy consumed by all MDCs. LOAF outperforms all baselines for varying R, N seg , N MDC and ISDV . Figure 9-(a) shows that ToCS, LEEF and LOAF require less energy as R increases, unlike FOCUS and MINDS which pursue a mst-based inter-cluster topology. Enlarging the communication range of an MDC, R, helps to shorten the tour length in a star inter-cluster topology and in turn results in reducing the average energy consumption of MDCs. Meanwhile, the tour length is hardly affected under a mst-based inter-cluster topology. Thus, Figures 9-(a) and 10-(a) evidently show that LOAF groups segments in an energy-efficient and balanced way. For instance, LOAF requires about 300% less energy and achieves approximately 480% more energy-balanced clustering in comparison to ToCS.

3) AVERAGE ENERGY CONSUMPTION OF ALL MDCs
In addition, larger values of N seg or ISDV require more MDC energy for all approaches as seen in Figure 9-(b) and 9-(d), respectively. This is expected because serving more segments or delivering more inter-segment data traffic would enlarge a total tour length and/or data loading time for MDCs. Figure 9-(c) shows another advantage of a star topology where the energy overhead diminishes dramatically as N MDC grows. We note that for small values of N MDC , LOAF achieves outstanding reduction in the energy overhead as compared to ToCS and LEEF. Such superiority is attributed to the energy-centric design principle of LOAF which strives to place a central cluster at the energy balanced center of all segments and based on which the formation of non-central clusters is optimized. Figure 10 demonstrates the network lifetime during which the formed topology by each algorithm normally operates.

4) NETWORK LIFETIME (NL)
In other words, it shows how long the MDCs tour as planned after federation and thus every pair of inter-segment communication is maintained. We study the effect of R, N seg , N MDC , and ISDV on NL, measured as (initE−AEC)

BPC
, where initE and BPC are set as 54400 Joule and 0.5 Joule/sec respectively. The results shown in Figure 10 are very much expected. Basically, LOAF yields the longest network lifetime in all cases and the results are consistent with Figure 9 where LOAF outperforms all baselines in terms of the average energy consumption. Figure 11 presents the maximum buffer requirement of rendezvous segments while delivering the inter-cluster data traffic. Therefore, this performance metric is applicable to only FOCUS, MINDS, LEEF and LOAF in which an MDC uploads/downloads the inter-cluster data from/at a buffer of a segment that is to be visited by another MDC serving a different cluster. As seen in Figure 11, LOAF requires the least buffer space regardless of R, N seg , N MDC and ISDV . This is because LOAF opts to not only reduce inter-cluster data traffic by keeping a pair of segments that exchange large data volume in the same cluster but also place a central cluster at the energy-balanced location considering the inter-segment traffic volume. Such design diminishes the buffer requirement of segments at rendezvous points. Figure 11-(a) shows how the buffer space requirement is affected by the communication range of an MDC, i.e., R. For FOCUS, MINDS and LOAF little change can be observed because R does not have a direct influence on a count of   segments belonging to a cluster or the inter-cluster data traffic volume; particularly, the latter affects the maximum buffer space of segments at rendezvous points. In addition, LOAF yields better performance than FOCUS, MINDS and LEEF since it places a central cluster at a mass of inter-segment traffic demands and thus reduces burdens on the shared segment in the central cluster. It is worth noting that LEEF requires more buffers as R grows. This is because LEEF exploits a cellbased grid architecture where the size of a cell is determined by R and identifies the smallest set CS T of the selected cells that covers all segments, based on which a star-shaped cluster topology is formed. Thus, as R gets larger one cell in CS T  probably covers more segments which in turns requires more buffer space for storing the inter-cluster data if the cell is included in a central cluster.

5) BUFFER SPACE REQUIRED AT GATEWAY SEGMENTS
Moreover, as much expected and seen in Figure 11-(b) and 11-(d), larger buffer space is required for all approaches as N seg or ISDV rises due to the increased inter-segment data volume. Figure 11-(c) captures the effect of the number of MDCs. Growing N MDC implies more clusters, which in turn introduces more inter-cluster data traffic. Therefore, the shared segments need more buffer space as N MDC increases. Figure 12 captures the sensitivity of the performance to configuration parameters, R, N seg , N MDC and ISDV . In each chart, the left and right bars represent the results of minus and plus 50% variations from the base values for input parameters, i.e., R = 100, N seg = 30, N MDC = 9, ISDV = 4. As seen in Figure 12-(a), (b) and (c), an increment in the ISDV value seems to influence LOAF more than that of R, N seg , and N MDC for D max , energy balance between MDCs and the average energy consumption. This is because D max is determined by rendezvous time between MDCs which is primarily determined by the inter-segment data volume. The energy consumption and balance are also more affected by the data communication load between segments than the travel path. Thus, a 50% increase of ISDV from the baseline setting causes larger performance variations than other parameters. These results further confirm the importance of factoring in the data upload/offload overhead in the solutions, something that sets LOAF apart from competing approaches.

6) COMPARING THE IMPACT OF VARIOUS PARAMETERS ON LOAF
Meanwhile, Figure 12-(d) shows that N seg and N MDC have more effect on the maximum buffer size required at gateway segments than ISDV . This is because such a requirement is mostly determined by the formed topology, i.e., MDC travel paths to serve a group of segments, rather than the intersegment data volume. Figure 13 shows how LOAF and the baseline approaches respond to changes in the inter-segment data volume (ISDV) during operation. In the experiment, ISDV is initially set at 8 Mbps and later changes to 2, 16, or 64 Mbps. The other input parameters are fixed as R = 100, N seg = 30, N MDC = 9. With this setup, the initial energy-balanced cluster is formed in the first phase of LOAF considering 8 Mbps inter-segment data volume and maintained during the second phase where data volume between segments changes to 2, 16, or 64 Mbps. The same steps are applied to LEEF which also works based on clustering. As seen in Figure 13, LOAF maintains its superiority and outperforms LEEF as well as FOCUS, MINDS and ToCS even when the value of ISDV changes in terms of inter-segment data delivery latency, energy balance between MDCs and energy consumption of MDCs and required buffer space for MDCs.

VI. CONCLUSION
In this paper, we have studied the federation problem of disjoint WSN segments using a limited number (k) of mobile relays that provide intermittent inter-segment connectivity. We have proposed LOAF, a novel approach that groups the VOLUME 8, 2020 segments into k clusters and defines energy-efficient and also balanced tour paths for the mobile relays by factoring in both inter-segment data volume and proximity to the formed clusters. LOAF finally forms a star topology where a central cluster is located at the center of the area considering inter-segment data volumes as well as geographical distance between segments. The simulation results demonstrate that LOAF outperforms competing approaches in terms of the maximum inter-segment data delivery latency, energy balance among MDCs, average energy consumption of MDCs and network lifetime with a competitively small amount of buffer space requirement. The effectiveness of LOAF grows with larger MDC communication ranges, and with increased segment and MDC counts.