TY - GEN

T1 - Improved algorithms and combinatorial bounds for independent Feedback Vertex Set

AU - Agrawal, Akanksha

AU - Gupta, Sushmita

AU - Saurabh, Saket

AU - Sharma, Roohani

N1 - Publisher Copyright:
© 2016 Akanksha Agrawal, Sushmita Gupta, Saket Saurabh, and Roohani Sharma.

PY - 2017/2/1

Y1 - 2017/2/1

N2 - In this paper we study the "independent" version of the classic Feedback Vertex Set problem in the realm of parameterized algorithms and moderately exponential time algorithms. More precisely, we study the Independent Feedback Vertex Set problem, where we are given an undirected graph G on n vertices and a positive integer k, and the objective is to check if there is an independent feedback vertex set of size at most k. A set S ⊆ V (G) is called an independent feedback vertex set (ifvs) if S is an independent set and G\S is a forest. In this paper we design two deterministic exact algorithms for Independent Feedback Vertex Set with running times O∗(4.1481k)1 and O∗(1.5981n). In fact, the algorithm with O∗(1.5981n) running time finds the smallest sized ifvs, if an ifvs exists. Both the algorithms are based on interesting measures and improve the best known algorithms for the problem in their respective domains. In particular, the algorithm with running time O∗(4.1481k) is an improvement over the previous algorithm that ran in time O∗(5k). On the other hand, the algorithm with running time O∗(1.5981n) is the first moderately exponential time algorithm that improves over the naïve algorithm that enumerates all the subsets of V (G). Additionally, we show that the number of minimal ifvses in any graph on n vertices is upper bounded by 1.7485n.

AB - In this paper we study the "independent" version of the classic Feedback Vertex Set problem in the realm of parameterized algorithms and moderately exponential time algorithms. More precisely, we study the Independent Feedback Vertex Set problem, where we are given an undirected graph G on n vertices and a positive integer k, and the objective is to check if there is an independent feedback vertex set of size at most k. A set S ⊆ V (G) is called an independent feedback vertex set (ifvs) if S is an independent set and G\S is a forest. In this paper we design two deterministic exact algorithms for Independent Feedback Vertex Set with running times O∗(4.1481k)1 and O∗(1.5981n). In fact, the algorithm with O∗(1.5981n) running time finds the smallest sized ifvs, if an ifvs exists. Both the algorithms are based on interesting measures and improve the best known algorithms for the problem in their respective domains. In particular, the algorithm with running time O∗(4.1481k) is an improvement over the previous algorithm that ran in time O∗(5k). On the other hand, the algorithm with running time O∗(1.5981n) is the first moderately exponential time algorithm that improves over the naïve algorithm that enumerates all the subsets of V (G). Additionally, we show that the number of minimal ifvses in any graph on n vertices is upper bounded by 1.7485n.

KW - Enumeration

KW - Exact algorithm

KW - Fixed parameter tractable

KW - Independent feedback vertex set

UR - http://www.scopus.com/inward/record.url?scp=85014697236&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.IPEC.2016.2

DO - 10.4230/LIPIcs.IPEC.2016.2

M3 - Conference contribution

AN - SCOPUS:85014697236

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 11th International Symposium on Parameterized and Exact Computation, IPEC 2016

A2 - Guo, Jiong

A2 - Hermelin, Danny

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

T2 - 11th International Symposium on Parameterized and Exact Computation, IPEC 2016

Y2 - 24 August 2016 through 26 August 2016

ER -