Parameterized algorithms and kernels for rainbow matching

Sushmita Gupta, Sanjukta Roy, Saket Saurabh, Meirav Zehavi

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In this paper, we study the NP-complete colorful variant of the classical Matching problem, namely, the Rainbow Matching problem. Given an edge-colored graph G and a positive integer k, this problem asks whether there exists a matching of size at least k such that all the edges in the matching have distinct colors. We first develop a deterministic algorithm that solves Rainbow Matching on paths in time (equation represented) and polynomial space. This algorithm is based on a curious combination of the method of bounded search trees and a "divide-and-conquer-like" approach, where the branching process is guided by the maintenance of an auxiliary bipartite graph where one side captures "divided-and-conquered" pieces of the path. Our second result is a randomized algorithm that solves Rainbow Matching on general graphs in time O?(2k) and polynomial-space. Here, we show how a result by Björklund et al. [JCSS, 2017] can be invoked as a black box, wrapped by a probability-based analysis tailored to our problem. We also complement our two main results by designing kernels for Rainbow Matching on general and bounded-degree graphs.

Original languageEnglish
Title of host publication42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017
EditorsKim G. Larsen, Jean-Francois Raskin, Hans L. Bodlaender
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770460
DOIs
StatePublished - 1 Nov 2017
Externally publishedYes
Event42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017 - Aalborg, Denmark
Duration: 21 Aug 201725 Aug 2017

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume83
ISSN (Print)1868-8969

Conference

Conference42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017
Country/TerritoryDenmark
CityAalborg
Period21/08/1725/08/17

Keywords

  • 3-Dimensional Matching
  • 3-Set Packing
  • Bounded Search Trees
  • Divide-and-Conquer
  • Parameterized Algorithm
  • Rainbow Matching

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