Fast Distributed Algorithms for LP-Type Problems of Bounded Dimension

TL;DR

This paper introduces efficient distributed algorithms for LP-type problems in the gossip model, achieving logarithmic rounds with polylogarithmic communication, applicable to many geometric and combinatorial problems.

Contribution

It presents the first distributed algorithms with logarithmic rounds for LP-type problems of bounded dimension in the gossip model.

Findings

Algorithms run in logarithmic rounds.

Communication per node is polylogarithmic.

Applicable to a wide range of LP-type problems.

Abstract

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