TY - JOUR

T1 - Quick but Odd Growth of Cacti

AU - Kolay, Sudeshna

AU - Lokshtanov, Daniel

AU - Panolan, Fahad

AU - Saurabh, Saket

N1 - Funding Information:
The conference version of this paper has been published in the Proceedings of IPEC 2015. The research leading to these results has received funding from the European Research Council (ERC) via grants Rigorous Theory of Preprocessing, reference 267959 and PARAPPROX, reference 306992 and the Bergen Research Foundation via grant “Beating Hardness by Preprocessing”.
Publisher Copyright:
© 2017, Springer Science+Business Media New York.

PY - 2017/9/1

Y1 - 2017/9/1

N2 - Let F be a family of graphs. Given an n-vertex input graph G and a positive integer k, testing whether G has a vertex subset S of size at most k, 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 the family of forests of cacti or the family of forests of odd-cacti. A graph H is called a forest of cacti if every pair of cycles in H intersect on at most one vertex. Furthermore, a forest of cacti H is called a forest of odd cacti, if every cycle of H is of odd length. Let us denote by C and Codd, the families of forests of cacti and forests of odd cacti, 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 worst case run time 12 knO ( 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.

AB - Let F be a family of graphs. Given an n-vertex input graph G and a positive integer k, testing whether G has a vertex subset S of size at most k, 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 the family of forests of cacti or the family of forests of odd-cacti. A graph H is called a forest of cacti if every pair of cycles in H intersect on at most one vertex. Furthermore, a forest of cacti H is called a forest of odd cacti, if every cycle of H is of odd length. Let us denote by C and Codd, the families of forests of cacti and forests of odd cacti, 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 worst case run time 12 knO ( 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.

KW - Diamond Hitting Set

KW - Even Cycle Transversal

KW - Fixed parameter tractability

KW - Randomized algorithms

UR - http://www.scopus.com/inward/record.url?scp=85019019674&partnerID=8YFLogxK

U2 - 10.1007/s00453-017-0317-1

DO - 10.1007/s00453-017-0317-1

M3 - Article

AN - SCOPUS:85019019674

SN - 0178-4617

VL - 79

SP - 271

EP - 290

JO - Algorithmica

JF - Algorithmica

IS - 1

ER -