Detecting cuts in sensor networks

We propose a low overhead scheme for detecting a network partition or cut in a sensor network. Consider a network S of n sensors, modeled as points in a two-dimensional plane. An ε-cut, for any 0<ε<1, is a linear separation of εn nodes in S from a distinguished node, the base station. We show that the base station can detect whenever an ε-cut occurs by monitoring the status of just O(1/ε) nodes in the network. Our scheme is deterministic and it is free of false positives: no reported cut has size smaller than 1/2εn. Besides this combinatorial result, we also propose efficient algorithms for finding the O(1/ε) nodes that should act as sentinels, and report on our simulation results, comparing the sentinel algorithm with two natural schemes based on sampling.