research-article

Maximum weight induced matching in some subclasses of bipartite graphs

Authors:

Juhi Chaudhary,

Manav KashyapAuthors Info & Claims

Journal of Combinatorial Optimization, Volume 40, Issue 3

Pages 713 - 732

https://doi.org/10.1007/s10878-020-00611-2

Published: 01 October 2020 Publication History

Abstract

A subset

M \subseteq E

of edges of a graph

G = (V, E)

is called a matching in G if no two edges in M share a common vertex. A matching M in G is called an induced matching if G[M], the subgraph of G induced by M, is the same as G[S], the subgraph of G induced by

S = {v \in V |

v is incident on an edge of

M}

. The Maximum Induced Matching problem is to find an induced matching of maximum cardinality. Given a graph G and a positive integer k, the Induced Matching Decision problem is to decide whether G has an induced matching of cardinality at least k. The Maximum Weight Induced Matching problem in a weighted graph

G = (V, E)

in which the weight of each edge is a positive real number, is to find an induced matching such that the sum of the weights of its edges is maximum. It is known that the Induced Matching Decision problem and hence the Maximum Weight Induced Matching problem is known to be NP-complete for general graphs and bipartite graphs. In this paper, we strengthened this result by showing that the Induced Matching Decision problem is NP-complete for star-convex bipartite graphs, comb-convex bipartite graphs, and perfect elimination bipartite graphs, the subclasses of the class of bipartite graphs. On the positive side, we propose polynomial time algorithms for the Maximum Weight Induced Matching problem for circular-convex bipartite graphs and triad-convex bipartite graphs by making polynomial time reductions from the Maximum Weight Induced Matching problem in these graph classes to the Maximum Weight Induced Matching problem in convex bipartite graphs.

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Cited By

Chaudhary JZehavi M(2023)Parameterized Results on Acyclic Matchings with Implications for Related ProblemsGraph-Theoretic Concepts in Computer Science10.1007/978-3-031-43380-1_15(201-216)Online publication date: 28-Jun-2023
https://dl.acm.org/doi/10.1007/978-3-031-43380-1_15
Klemz BRote G(2022)Linear-Time Algorithms for Maximum-Weight Induced Matchings and Minimum Chain Covers in Convex Bipartite GraphsAlgorithmica10.1007/s00453-021-00904-w84:4(1064-1080)Online publication date: 1-Apr-2022
https://dl.acm.org/doi/10.1007/s00453-021-00904-w
Gomes GMasquio BPinto PSantos VSzwarcfiter J(2022)Weighted Connected MatchingsLATIN 2022: Theoretical Informatics10.1007/978-3-031-20624-5_4(54-70)Online publication date: 7-Nov-2022
https://dl.acm.org/doi/10.1007/978-3-031-20624-5_4
Show More Cited By

Index Terms

Maximum weight induced matching in some subclasses of bipartite graphs
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
      1. Combinatorial algorithms
    2. Graph theory
      1. Graph algorithms
      2. Graph enumeration
2. Theory of computation
  1. Design and analysis of algorithms
  2. Randomness, geometry and discrete structures

Index terms have been assigned to the content through auto-classification.

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cover image Journal of Combinatorial Optimization

Journal of Combinatorial Optimization Volume 40, Issue 3

Oct 2020

290 pages

ISSN:1382-6905

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© Springer Science+Business Media, LLC, part of Springer Nature 2020.

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 October 2020

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Cited By

Chaudhary JZehavi M(2023)Parameterized Results on Acyclic Matchings with Implications for Related ProblemsGraph-Theoretic Concepts in Computer Science10.1007/978-3-031-43380-1_15(201-216)Online publication date: 28-Jun-2023
https://dl.acm.org/doi/10.1007/978-3-031-43380-1_15
Klemz BRote G(2022)Linear-Time Algorithms for Maximum-Weight Induced Matchings and Minimum Chain Covers in Convex Bipartite GraphsAlgorithmica10.1007/s00453-021-00904-w84:4(1064-1080)Online publication date: 1-Apr-2022
https://dl.acm.org/doi/10.1007/s00453-021-00904-w
Gomes GMasquio BPinto PSantos VSzwarcfiter J(2022)Weighted Connected MatchingsLATIN 2022: Theoretical Informatics10.1007/978-3-031-20624-5_4(54-70)Online publication date: 7-Nov-2022
https://dl.acm.org/doi/10.1007/978-3-031-20624-5_4
Bonomo-Braberman FBrettell NMunaro APaulusma D(2021)Solving Problems on Generalized Convex Graphs via Mim-WidthAlgorithms and Data Structures10.1007/978-3-030-83508-8_15(200-214)Online publication date: 9-Aug-2021
https://dl.acm.org/doi/10.1007/978-3-030-83508-8_15

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