Abstract

The Subset Feedback Vertex Set problem (SFVS) takes an n-vertex graph G=(V,E), a terminal set T⊆V, and an integer k as the input. The goal is to determine whether there exists a subset S⊆V of at most k vertices whose removal makes no terminal in T contained in a cycle in the remaining graph. When T=V, SFVS degenerates to the classical Feedback Vertex Set problem (FVS). Both SFVS and FVS have been extensively studied in parameterized algorithms. In this paper, we study parameterized algorithms for Subset Feedback Vertex Set in Tournaments (SFVST), i.e., SFVS with the restriction that the input graph is always a tournament. By using the iterative compression method and a novel dynamic programming, we show that SFVST can be solved in 2k+o(k)nO(1) time, improving the bound obtained from 3-Hitting Set.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.