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O(n) Time Algorithms for Dominating Induced Matching Problems

  • Min Chih Lin
  • Michel J. Mizrahi
  • Jayme L. Szwarcfiter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8392)

Abstract

We describe O(n) time algorithms for finding the minimum weighted dominating induced matching of chordal, dually chordal, biconvex, and claw-free graphs. For the first three classes, we prove tight O(n) bounds on the maximum number of edges that a graph having a dominating induced matching may contain. By applying these bounds, countings and employing existing O(n + m) time algorithms we show that they can be reduced to O(n) time. For claw–free graphs, we describe an algorithm based on that by Cardoso, Korpelainen and Lozin [4], for solving the unweighted version of the problem, which decreases its complexity from O(n 2) to O(n), while additionally solving the weighted version.

Keywords

algorithms dominating induced matchings graph theory 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Min Chih Lin
    • 1
  • Michel J. Mizrahi
    • 1
  • Jayme L. Szwarcfiter
    • 2
    • 3
  1. 1.CONICET, Instituto de Cálculo and Departamento de ComputaciónUniversidad de Buenos AiresBuenos AiresArgentina
  2. 2.I. Mat., COPPE and NCEUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil
  3. 3.Qualidade e TecnologiaInstituto Nacional de MetrologiaRio de JaneiroBrazil

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