Kernels for Feedback Arc Set In Tournaments
Abstract
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 e>0, the kernelized instance has at most (2+e)k vertices. Our result improves the previous known bound of O(k^2) on the kernel size for k-FAST. Our kernelization algorithm solves the problem on a subclass of tournaments in polynomial time and uses a known polynomial time approximation scheme for k-FAST.
Cite
@article{arxiv.0907.2165,
title = {Kernels for Feedback Arc Set In Tournaments},
author = {Stéphane Bessy and Fedor V. Fomin and Serge Gaspers and Christophe Paul and Anthony Perez and Saket Saurabh and Stéphan Thomassé},
journal= {arXiv preprint arXiv:0907.2165},
year = {2009}
}