Rigid Network Design Via Submodular Set Function Optimization

Abstract

We consider the problem of constructing networks that exhibit desirable algebraic rigidity properties, which can provide significant performance improvements for associated formation shape control and localization tasks. We show that the network design problem can be formulated as a submodular set function optimization problem and propose greedy algorithms that achieve global optimality or an established near-optimality guarantee. We also consider the separate but related problem of selecting anchors for sensor network localization to optimize a metric of the error in the localization solutions. We show that an interesting metric is a modular set function, which allows a globally optimal sel..