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

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.",

keywords = "Parameterized complexity, Polynomial kernel, Rainbow matching",

author = "Sushmita Gupta and Sanjukta Roy and Saket Saurabh and Meirav Zehavi",

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T1 - Quadratic Vertex Kernel for Rainbow Matching

AU - Gupta, Sushmita

AU - Roy, Sanjukta

AU - Saurabh, Saket

AU - Zehavi, Meirav

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Y1 - 2020/4/1

N2 - 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.

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.

KW - Parameterized complexity

KW - Polynomial kernel

KW - Rainbow matching

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SP - 881

EP - 897

JO - Algorithmica

JF - Algorithmica

IS - 4

ER -

Quadratic Vertex Kernel for Rainbow Matching

Abstract

Keywords

ASJC Scopus subject areas

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