TY - GEN
T1 - Parameterized algorithms and kernels for rainbow matching
AU - Gupta, Sushmita
AU - Roy, Sanjukta
AU - Saurabh, Saket
AU - Zehavi, Meirav
N1 - Publisher Copyright:
© Sushmita Gupta, Sanjukta Roy, Saket Saurabh, and Meirav Zehavi; licensed under Creative Commons License CC-BY.
PY - 2017/11/1
Y1 - 2017/11/1
N2 - 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.
AB - 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.
KW - 3-Dimensional Matching
KW - 3-Set Packing
KW - Bounded Search Trees
KW - Divide-and-Conquer
KW - Parameterized Algorithm
KW - Rainbow Matching
UR - http://www.scopus.com/inward/record.url?scp=85038424454&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.MFCS.2017.71
DO - 10.4230/LIPIcs.MFCS.2017.71
M3 - Conference contribution
AN - SCOPUS:85038424454
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017
A2 - Larsen, Kim G.
A2 - Raskin, Jean-Francois
A2 - Bodlaender, Hans L.
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 42nd International Symposium on Mathematical Foundations of Computer Science, MFCS 2017
Y2 - 21 August 2017 through 25 August 2017
ER -