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In this paper we present various distributed algorithms for LP-type problemsin the well-known gossip model. LP-type problems include many important classesof problems such as (integer) linear programming, geometric problems likesmallest enclosing ball and polytope distance, and set problems like hittingset and set cover. In the gossip model, a node can only push information to orpull information from nodes chosen uniformly at random. Protocols for thegossip model are usually very practical due to their fast convergence, theirsimplicity, and their stability under stress and disruptions. Our algorithmsare very efficient (logarithmic rounds or better with just polylogarithmiccommunication work per node per round) whenever the combinatorial dimension ofthe given LP-type problem is constant, even if the size of the given LP-typeproblem is polynomially large in the number of nodes.

Fast Distributed Algorithms for LP-Type Problems of Bounded Dimension