Tightness of LP via Max-product Belief Propagation
<|reference_start|>Tightness of LP via Max-product Belief Propagation: 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 $G(n,c/n)$ for $c \leq 2e$ and random regular graph $G(n,r)$ for $r\leq 4$ 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.<|reference_end|>
@article{sanghavi2005tightness,
    title={Tightness of LP via Max-product Belief Propagation},
    author={Sujay Sanghavi and Devavrat Shah},
    journal={arXiv preprint arXiv:cs/0508097},
    year={2005},
    archivePrefix={arXiv},
    eprint={cs/0508097},
    primaryClass={cs.DS cs.DM}
}