Quadratic Vertex Kernel for Rainbow Matching

Sushmita Gupta; Sanjukta Roy; Saket Saurabh; Meirav Zehavi

doi:10.1007/s00453-019-00618-0

Quadratic Vertex Kernel for Rainbow Matching

Sushmita Gupta, Sanjukta Roy, Saket Saurabh, Meirav Zehavi

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 language	English
Pages (from-to)	881-897
Number of pages	17
Journal	Algorithmica
Volume	82
Issue number	4
DOIs	https://doi.org/10.1007/s00453-019-00618-0
State	Published - 1 Apr 2020

Keywords

Parameterized complexity
Polynomial kernel
Rainbow matching

ASJC Scopus subject areas

General Computer Science
Computer Science Applications
Applied Mathematics

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10.1007/s00453-019-00618-0

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title = "Quadratic Vertex Kernel for Rainbow Matching",

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{\textquoteright}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.",

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AU - Roy, Sanjukta

AU - Saurabh, Saket

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AB - 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.

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Quadratic Vertex Kernel for Rainbow Matching

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Keywords

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