Work

A Weighted Linear Matroid Parity Algorithm

Year: 2019

Type: preprint

Abstract: The matroid parity (or matroid matching) problem, introduced as a common generalization of matching and matroid intersection problems, is so general that it requires an exponential number of oracle calls. Nevertheless, Lovász (1980) showed that this problem admits a min-max formula and a polynomial algorithm for linearly represented matroids. Since then efficient algorithms have been developed for the linear matroid parity problem. In this paper, we present a combinatorial, deterministic, polynomial-time algorithm for the weighted linear matroid parity problem. The algorithm builds on a polynomial matrix formulation using Pfaffian and adopts a primal-dual approach based on the augmenting path algorithm of Gabow and Stallmann (1986) for the unweighted problem.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1905.13371

Authors: Iwata, Satoru, Kobayashi, Yusuke

Institutions: The University of Tokyo, Kyoto University, Research Institute for Mathematical Sciences, Kyoto University

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Ministry of Education, Culture, Sports, Science and Technology, Japan Society for the Promotion of Science, Core Research for Evolutional Science and Technology

Awards: G1712086689, G1826640924, G2976975559, G3514450815, G3827949265, Study on Theory of Combinatorial Optimization with Applications to Robust Network Design, G6718509927, G7346436297, G7445383500, G7879866177, G7996441422, G8051431865

OpenAlex ID: W2950665492

Cites: 31

Cited by:

Related to: 10