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On the correlation gap of matroids

Husić, Edin ORCID: 0000-0002-6708-5112, Koh, Zhuan Khye, Loho, Georg and Végh, László A. ORCID: 0000-0003-1152-200X (2023) On the correlation gap of matroids. In: Del Pia, Alberto and Kaibel, Volker, (eds.) Integer Programming and Combinatorial Optimization - 24th International Conference, IPCO 2023, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Science and Business Media Deutschland GmbH, pp. 203-216. ISBN 9783031327254

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Identification Number: 10.1007/978-3-031-32726-1_15

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: Book Section
Additional Information: © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Date Deposited: 25 Jul 2023 10:03
Last Modified: 26 Nov 2023 01:42
URI: http://eprints.lse.ac.uk/id/eprint/119824

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