Fixed-parameter tractability results for feedback set problems in tournaments

• Published in: Journal of discrete algorithms (Amsterdam, Netherlands) Vol. 8; no. 1; pp. 76 - 86
• Main Authors: Dom, Michael, Guo, Jiong, Hüffner, Falk, Niedermeier, Rolf, Truss, Anke
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.03.2010
• Subjects: Bipartite tournament; Feedback arc set; Feedback vertex set; Fixed-parameter tractability; Iterative compression; Tournament; Bipartite tournament; Iterative compression; Feedback arc set; Feedback vertex set; Tournament; Fixed-parameter tractability
• ISSN: 1570-8667; 1570-8675
• DOI: 10.1016/j.jda.2009.08.001

Complementing recent progress on classical complexity and polynomial-time approximability of feedback set problems in (bipartite) tournaments, we extend and improve fixed-parameter tractability results for these problems. We show that Feedback Vertex Set in tournaments (FVST) is amenable to the novel iterative compression technique, and we provide a depth-bounded search tree for Feedback Arc Set in bipartite tournaments based on a new forbidden subgraph characterization. Moreover, we apply the iterative compression technique to d- Hitting Set, which generalizes Feedback Vertex Set in tournaments, and obtain improved upper bounds for the time needed to solve 4- Hitting Set and 5- Hitting Set. Using our parameterized algorithm for Feedback Vertex Set in tournaments, we also give an exact (not parameterized) algorithm for it running in O ( 1.709 n ) time, where n is the number of input graph vertices, answering a question of Woeginger [G.J. Woeginger, Open problems around exact algorithms, Discrete Appl. Math. 156 (3) (2008) 397–405].