A Unified Framework for Constrained Linearization of Sensor Networks With Arbitrary Shapes

In such application scenarios of sensor networks as motion planing of a mobile robot for data collection or battery recharging, the robot is often required to start from a pre-required location (referred to as
Entrance
) and quit at another pre-required location (referred to as
Exit
) before visiting all sensors. Existing solutions can only compute a traversal path (i.e., a space-filling curve, SFC) linking all sensors for either 2D sensor networks or 3D surface/volume networks, where the Entrance and the Exit cannot be specified beforehand. As such, in this paper, we study the constrained linearization problem of sensor networks, i.e., computing a path (referred to as
constrained space-filling curve
, CSFC) traversing all sensors, starting from the Entrance and ending at the Exit. Motivated by the generation of SFCs in Fractal Geometry, we propose a unified framework, which is novel, simple yet efficient, for the constrained linearization of 2D sensor networks or 3D surface/volume sensor networks merely using connectivity information in an iterative fashion. Specifically, we first compute a shortest path between the Entrance and the Exit via in-network flooding to initialize the CSFC; then, during each round, we simultaneously
deform
the edges (i.e., replacing each edge with a zig-zag pattern) on the CSFC until no edges can be deformed, and a coarse CSFC, possibly
missing
some sensors (e.g., due to network sparsity or irregularity), is thus derived. We finally propose to connect the unvisited sensors into the coarse CSFC, and the network is linearized such that all nodes are orderly traversed by the CSFC from the Entrance to the Exit. Extensive simulations show that: 1) our algorithm can efficiently compute the CSFC for 2D sensor networks and 3D surface/volume sensor networks in terms of once-visited node number and time/message complexity, etc., 2) our algorithm is robust to many factors such as network shape, density, scale and communication radio model, etc., and 3) our approach outperforms the state-of-the-art SURF
[19]
, a Space filling cURve computing algorithm for high genus 3D surFace sensor networks, where the constraint on the Entrance and the Exit is not considered.