The cutting plane method is polynomial for perfect matchings

Chandrasekaran, Karthekeyan, Végh, László A. ORCID: 0000-0003-1152-200X and Vempala, Santosh S. (2016) The cutting plane method is polynomial for perfect matchings. Mathematics of Operations Research, 41 (1). pp. 23-48. ISSN 0364-765X

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Abstract

The cutting plane approach to finding minimum-cost perfect matchings has been discussed by several authors over past decades. Its convergence has been an open question. We develop a cutting plane algorithm that converges in polynomial-time using only Edmonds’ blossom inequalities, and which maintains half-integral intermediate LP solutions supported by a disjoint union of odd cycles and edges. Our main insight is a method to retain only a subset of the previously added cutting planes based on their dual values. This allows us to quickly find violated blossom inequalities and argue convergence by tracking the number of odd cycles in the support of intermediate solutions

Item Type:	Article
Official URL:	http://pubsonline.informs.org/journal/moor
Additional Information:	© 2016 INFORMS
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	14 Apr 2016 11:57
Last Modified:	12 Dec 2024 01:00
Projects:	AF0915903, 0914732
Funders:	National Science Foundation, National Science Foundation
URI:	http://eprints.lse.ac.uk/id/eprint/66123

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