Distributed online submodular maximization in resource-constrained networks

Abstract

Maximization of submodular set functions arises in wireless applications such as scheduling, caching, and leader selection. For a centralized entity with oracle access to the submodular function, submodular maximization can be approximated up to a constant factor using polynomial-time algorithms; such an entity, however, may be unavailable in decentralized wireless networks. In this paper, we consider maximization of a time-varying submodular function by distributed, resource-constrained nodes. We present algorithms for unconstrained distributed submodular maximization, as well as monotone submodular maximization subject to cardinality constraints. For the unconstrained submodular maximization problem, our algorithm achieves an expected optimality gap of 1/3. For cardinality-constrained submodular maximization, our algorithm achieves an expected optimality gap of 1/2, while reducing the storage and communication overhead, as well as the computation requirements of the nodes, compared to existing techniques. We evaluate our approach through an experimental study using sensor scheduling data, and find that our approach is within ten percent of the best achievable utility in the unconstrained case and within five percent in the constrained case.