On the correlation gap of matroids

Koh, Zhuan Khye, Husic, Edin ORCID: 0000-0002-6708-5112, Loho, Georg and Végh, László A. ORCID: 0000-0003-1152-200X (2024) On the correlation gap of matroids. Mathematical Programming. ISSN 0025-5610

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Abstract

A set function can be extended to the unit cube in various ways; the correlation gap measures the ratio between two natural extensions. This quantity has been identified as the performance guarantee in a range of approximation algorithms and mechanism design settings. It is known that the correlation gap of a monotone submodular function is at least 1-1/e, and this is tight for simple matroid rank functions. We initiate a fine-grained study of the correlation gap of matroid rank functions. In particular, we present an improved lower bound on the correlation gap as parametrized by the rank and girth of the matroid. We also show that for any matroid, the correlation gap of its weighted rank function is minimized under uniform weights. Such improved lower bounds have direct applications for submodular maximization under matroid constraints, mechanism design, and contention resolution schemes.

Item Type:	Article
Official URL:	https://link.springer.com/journal/10107
Additional Information:	© 2024 The Author(s)
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	02 Jul 2024 13:12
Last Modified:	12 Dec 2024 04:21
URI:	http://eprints.lse.ac.uk/id/eprint/124089

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