Algorithms to Approximate Column-Sparse Packing Problems
Abstract
Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation algorithms for some well-known families of such problems. As three main examples, we attain the integrality gap, up to lower-order terms, for known LP relaxations for k-column sparse packing integer programs (Bansal et al., Theory of Computing, 2012) and stochastic k-set packing (Bansal et al., Algorithmica, 2012), and go "half the remaining distance" to optimal for a major integrality-gap conjecture of Furedi, Kahn and Seymour on hypergraph matching (Combinatorica, 1993).
Cite
@article{arxiv.1711.02724,
title = {Algorithms to Approximate Column-Sparse Packing Problems},
author = {Brian Brubach and Karthik Abinav Sankararaman and Aravind Srinivasan and Pan Xu},
journal= {arXiv preprint arXiv:1711.02724},
year = {2019}
}
Comments
Extended abstract appeared in SODA 2018. Full version in ACM Transactions of Algorithms