Distributed Combinatorial Optimization – Extended Abstract

Approximating integer linear programs by solving a relaxation to a linear program (LP) and afterwards reconstructing an integer solution from the fractional one is a standard technique in a non-distributed scenario. Surprisingly, the method has not often been applied for distributed algorithms. In this paper, we show that LP relaxation is a powerful technique also to obtain fast distributed approximation algorithms. We present a novel deterministic distributed algorithm which computes a constant factor approximates for fractional covering and packing problems in only log rounds, using messages of logarithmic size. If messages are allowed to be larger, we show that a constant approximation can be achieved in a logarithmic number of rounds only. Finally, we show that by combining our LP approximation algorithms with randomized rounding techniques, we obtain efficient distributed approximation algorithms for a number of combinatorial problems.