Efficient algorithms for maximum induced matching problem in permutation and trapezoid graphs

We first design an \(\mathcal{O}(n^2)\) solution for finding a maximum induced matching in permutation graphs given their permutation models, based on a dynamic programming algorithm with the aid of the sweep line technique. With the support of the disjoint-set data structure, we improve the complex...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2021-11
Main Authors: Nguyen, Viet Dung, Ba Thai Pham, Phan Thuan Do
Format: Article
Language:English
Subjects:
Algorithms
Data structures
Dynamic programming
Graph matching
Graphs
Permutations
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We first design an \(\mathcal{O}(n^2)\) solution for finding a maximum induced matching in permutation graphs given their permutation models, based on a dynamic programming algorithm with the aid of the sweep line technique. With the support of the disjoint-set data structure, we improve the complexity to \(\mathcal{O}(m + n)\). Consequently, we extend this result to give an \(\mathcal{O}(m + n)\) algorithm for the same problem in trapezoid graphs. By combining our algorithms with the current best graph identification algorithms, we can solve the MIM problem in permutation and trapezoid graphs in linear and \(\mathcal{O}(n^2)\) time, respectively. Our results are far better than the best known \(\mathcal{O}(mn)\) algorithm for the maximum induced matching problem in both graph classes, which was proposed by Habib et al.
ISSN:2331-8422
DOI:10.48550/arxiv.2107.08480