The parameterized complexity of cycle packing: Indifference is not an issue

R. Krithika, Abhishek Sahu, Saket Saurabh, Meirav Zehavi

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

Abstract

In the Cycle Packing problem, we are given an undirected graph G, a positive integer r, and the task is to check whether there exist r vertex-disjoint cycles. In this paper, we study Cycle Packing with respect to a structural parameter, namely, distance to proper interval graphs (indifference graphs). In particular, we show that Cycle Packing is fixed-parameter tractable (FPT) when parameterized by t, the size of a proper interval deletion set. For this purpose, we design an algorithm with O(2 O(t log t)nO(1)) running time. Several structural parameterizations for Cycle Packing have been studied in the literature and our FPT algorithm fills a gap in the ecology of such parameterizations. We combine color coding, greedy strategy and dynamic programming based on structural properties of proper interval graphs in a non-trivial fashion to obtain the FPT algorithm.

Original languageEnglish
Title of host publicationLATIN 2018
Subtitle of host publicationTheoretical Informatics - 13th Latin American Symposium, Proceedings
EditorsMiguel A. Mosteiro, Michael A. Bender, Martin Farach-Colton
PublisherSpringer Verlag
Pages712-726
Number of pages15
ISBN (Print)9783319774039
DOIs
StatePublished - 1 Jan 2018
Event13th International Symposium on Latin American Theoretical Informatics, LATIN 2018 - Buenos Aires, Argentina
Duration: 16 Apr 201819 Apr 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10807 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference13th International Symposium on Latin American Theoretical Informatics, LATIN 2018
Country/TerritoryArgentina
CityBuenos Aires
Period16/04/1819/04/18

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