Tightness of LP via Max-product Belief Propagation
Data Structures and Algorithms
2008-04-14 v2 Discrete Mathematics
Abstract
We investigate the question of tightness of linear programming (LP) relaxation for finding a maximum weight independent set (MWIS) in sparse random weighted graphs. We show that an edge-based LP relaxation is asymptotically tight for Erdos-Renyi graph for and random regular graph for when node weights are i.i.d. with exponential distribution of mean 1. We establish these results, through a precise relation between the tightness of LP relaxation and convergence of the max-product belief propagation algorithm. We believe that this novel method of understanding structural properties of combinatorial problems through properties of iterative procedure such as the max-product should be of interest in its own right.
Keywords
Cite
@article{arxiv.cs/0508097,
title = {Tightness of LP via Max-product Belief Propagation},
author = {Sujay Sanghavi and Devavrat Shah},
journal= {arXiv preprint arXiv:cs/0508097},
year = {2008}
}