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We propose distributed algorithms to automatically deploy a group of roboticagents and provide coverage of a discretized environment represented by agraph. The classic Lloyd approach to coverage optimization involves separatecentering and partitioning steps and converges to the set of centroidal Voronoipartitions. In this work we present a novel graph coverage algorithm whichachieves better performance without this separation while requiring onlypairwise ``gossip'' communication between agents. Our new algorithm provablyconverges to an element of the set of pairwise-optimal partitions, a subset ofthe set of centroidal Voronoi partitions. We illustrate that this newequilibrium set represents a significant performance improvement throughnumerical comparisons to existing Lloyd-type methods. Finally, we discuss waysto efficiently do the necessary computations.

Pairwise Optimal Discrete Coverage Control for Gossiping Robots