Quadratic Vertex Kernel for Rainbow Matching

Sushmita Gupta, Sanjukta Roy, Saket Saurabh, Meirav Zehavi

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we study the NP-complete colorful variant of the classic matching problem, namely, the Rainbow Matching problem. Given an edge-colored graph G and a positive integer k, the goal is to decide whether there exists a matching of size at least k such that the edges in the matching have distinct colors. Previously, in [MFCS’17], we studied this problem from the view point of Parameterized Complexity and gave efficient FPT algorithms as well as a quadratic kernel on paths. In this paper we design a quadratic vertex kernel for Rainbow Matching on general graphs; generalizing the earlier quadratic kernel on paths to general graphs. For our kernelization algorithm we combine a graph decomposition method with an application of expansion lemma.

Original languageEnglish
JournalAlgorithmica
DOIs
StatePublished - 1 Jan 2019

Keywords

  • Parameterized complexity
  • Polynomial kernel
  • Rainbow matching

ASJC Scopus subject areas

  • Computer Science (all)
  • Computer Science Applications
  • Applied Mathematics

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