Local Approximation Algorithms for Scheduling Problems in Sensor Networks

We study fractional scheduling problems in sensor networks, in particular, sleep scheduling (generalisation of fractional domatic partition) and activity scheduling (generalisation of fractional graph colouring). The problems are hard to solve in general even in a centralised setting; however, we show that there are practically relevant families of graphs where these problems admit a local distributed approximation algorithm; in a local algorithm each node utilises information from its constant-size neighbourhood only. Our algorithm does not need the spatial coordinates of the nodes; it suffices that a subset of nodes is designated as markers during network deployment. Our algorithm can be applied in any marked graph satisfying certain bounds on the marker density; if the bounds are met, guaranteed near-optimal solutions can be found in constant time, space and communication per node. We also show that auxiliary information is necessary—no local algorithm can achieve a satisfactory approximation guarantee on unmarked graphs.