Node Placement to Maximize Reliability of a Communication Network with Application to Satellite Swarms

The structure of a mobile ad hoc network changes dynamically based on node positioning. We consider a setting in which nodes can communicate if they are within a prescribed distance of one another, giving rise to a communication network. An example is a swarm of small satellites that cooperate to perform tasks; such swarms are likely to become commonplace in space missions. In this paper, we consider the problem of adding a new node or repositioning a current node in the network while optimizing a given network parameter such as network reliability. Although there are infinitely many locations to place the new node in space, there are only finitely many possible changes to the communication network. We provide an algorithm that enumerates all possible network changes in time O(
$n$

²
log n) or O(
$n$
³
log n), for networks in 2- or 3-dimensional Euclidean space, respectively. We apply the proposed algorithm to a satellite swarm formation planning problem, where the goal is to maximize network reliability.