TY - GEN

T1 - Quick but odd growth of cacti

AU - Kolay, Sudeshna

AU - Lokshtanov, Daniel

AU - Panolan, Fahad

AU - Saurabh, Saket

N1 - Publisher Copyright:
© Sudeshna Kolay, Daniel Lokshtanov, Fahad Panolan, and Saket Saurabh;.

PY - 2015/11/1

Y1 - 2015/11/1

N2 - 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.

AB - 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.

KW - Diamond hitting set

KW - Even cycle transversal

KW - Randomized algorithms

UR - http://www.scopus.com/inward/record.url?scp=84958250201&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.IPEC.2015.258

DO - 10.4230/LIPIcs.IPEC.2015.258

M3 - Conference contribution

AN - SCOPUS:84958250201

T3 - Leibniz International Proceedings in Informatics, LIPIcs

SP - 258

EP - 269

BT - 10th International Symposium on Parameterized and Exact Computation, IPEC 2015

A2 - Husfeldt, Thore

A2 - Husfeldt, Thore

A2 - Kanj, Iyad

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 10th International Symposium on Parameterized and Exact Computation, IPEC 2015

Y2 - 16 September 2015 through 18 September 2015

ER -