Quick but odd growth of cacti

Sudeshna Kolay, Daniel Lokshtanov, Fahad Panolan, Saket Saurabh

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

2 Scopus citations

Abstract

Let F be a family of graphs. Given an input graph G and a positive integer κ, testing whether G has a κ-sized subset of vertices S, such that G\ S belongs to F, is a prototype vertex deletion problem. These type of problems have attracted a lot of attention in recent times in the domain of parameterized complexity. In this paper, we study two such problems; when F is either a family of cactus graphs or a family of odd-cactus graphs. A graph H is called a cactus graph if every pair of cycles in H intersect on at most one vertex. Furthermore, a cactus graph H is called an odd cactus, if every cycle of H is of odd length. Let us denote by C and Codd, families of cactus and odd cactus, respectively. The vertex deletion problems corresponding to C and Codd are called Diamond Hitting Set and Even Cycle Transversal, respectively. In this paper we design randomized algorithms with running time 12κnO(1) for both these problems. Our algorithms considerably improve the running time for Diamond Hitting Set and Even Cycle Transversal, compared to what is known about them.

Original languageEnglish
Title of host publication10th International Symposium on Parameterized and Exact Computation, IPEC 2015
EditorsThore Husfeldt, Thore Husfeldt, Iyad Kanj
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages258-269
Number of pages12
ISBN (Electronic)9783939897927
DOIs
StatePublished - 1 Nov 2015
Externally publishedYes
Event10th International Symposium on Parameterized and Exact Computation, IPEC 2015 - Patras, Greece
Duration: 16 Sep 201518 Sep 2015

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume43
ISSN (Print)1868-8969

Conference

Conference10th International Symposium on Parameterized and Exact Computation, IPEC 2015
Country/TerritoryGreece
CityPatras
Period16/09/1518/09/15

Keywords

  • Diamond hitting set
  • Even cycle transversal
  • Randomized algorithms

ASJC Scopus subject areas

  • Software

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