Kernels for Feedback Arc Set In Tournaments

A tournament T = (V, A) is a directed graph in which there is exactly one arc between every pair of distinct vertices. Given a digraph on n vertices and an integer parameter k, the Feedback Arc Set problem asks whether the given digraph has a set of k arcs whose removal results in an acyclic digraph. The Feedback Arc Set problem restricted to tournaments is known as the k-Feedback Arc Set in Tournaments (k-FAST) problem. In this paper we obtain a linear vertex kernel for k-FAST. That is, we give a polynomial time algorithm which given an input instance T to k-FAST obtains an equivalent instance T on O(k) vertices. In fact, given any fixed > 0, the kernelized instance has at most (2 + )k vertices. Our result improves the previous known bound of O(k2 ) on the kernel size for k-FAST. For our kernelization algorithm we find a subclass of tournaments where one can find a minimum sized feedback arc set in polynomial time and use the known polynomial time approximation scheme for k-FAS...

• Type: Conference
• Year: 2009
• Where: FSTTCS
• Authors: Stéphane Bessy, Fedor V. Fomin, Serge Gaspers, Christophe Paul, Anthony Perez, Saket Saurabh, Stéphan Thomassé
• Keywords: Feedback Arc Set, Feedback Arc Set Problem, FSTTCS 2009, Polynomial Time, Theoretical Computer Science