Affiliation:
1. University of Maryland, College Park, Maryland, USA
2. University of Maryland, College Park and New Jersey Institute of Technology, New Jersey, USA
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 Füredi, Kahn, and Seymour on hypergraph matching (
Combinatorica
, 1993).
Funder
Google
Adobe Systems
Amazon Web Services
National Science Foundation
Publisher
Association for Computing Machinery (ACM)
Subject
Mathematics (miscellaneous)
Reference79 articles.
1. Marek Adamczyk. 2015. Non-negative submodular stochastic probing via stochastic contention resolution schemes. CoRR abs/1508.07771 (2015). Retrieved from: http://arxiv.org/abs/1508.07771. Marek Adamczyk. 2015. Non-negative submodular stochastic probing via stochastic contention resolution schemes. CoRR abs/1508.07771 (2015). Retrieved from: http://arxiv.org/abs/1508.07771.
2. Improved Approximation Algorithms for Stochastic Matching
3. Marek Adamczyk and Michał Włodarczyk. 2018. Random order contention resolution schemes. Retrieved from: arXiv preprint arXiv:1804.02584 (2018). Marek Adamczyk and Michał Włodarczyk. 2018. Random order contention resolution schemes. Retrieved from: arXiv preprint arXiv:1804.02584 (2018).
4. A note on Ramsey numbers
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