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Quick but Odd Growth of Cacti

Authors Sudeshna Kolay, Daniel Lokshtanov, Fahad Panolan, Saket Saurabh

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Sudeshna Kolay
Daniel Lokshtanov
Fahad Panolan
Saket Saurabh

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Sudeshna Kolay, Daniel Lokshtanov, Fahad Panolan, and Saket Saurabh. Quick but Odd Growth of Cacti. In 10th International Symposium on Parameterized and Exact Computation (IPEC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 43, pp. 258-269, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015) https://doi.org/10.4230/LIPIcs.IPEC.2015.258

Abstract

Let F be a family of graphs. Given an input graph G and a positive integer k, testing whether G has a k-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 C_{odd},  families of cactus and odd cactus, respectively. The vertex deletion problems corresponding to C and C_{odd} are called Diamond Hitting Set and Even Cycle Transversal, respectively. In this paper we design randomized algorithms with running time 12^{k}*n^{O(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.

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Keywords
  • Even Cycle Transversal
  • Diamond Hitting Set
  • Randomized Algorithms

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