On the kernelization of ranking r-CSP in tournaments
Anthony Perez · arXiv (Cornell University) · 2012
A Ranking r-Constraint Satisfaction Problem (ranking r-CSP) consists of a ground set of vertices V, an arity r > 2, a parameter k and a constraint system c, where c is a function which maps rankings of r-sized subsets of V to {0,1}. The objective is to decide if there exists a ranking of the vertices satisfying all but at most k constraints. Famous ranking r-CSP include the Feedback Arc Set in Tournaments and Betweenness in Tournaments problems. We consider these problems from the kernelization viewpoint. We prove that so-called l_r-simply characterized ranking r-CSP admit linear vertex-kernels whenever they admit constant-factor approximation algorithms. This implies that r-Betweenness in Tournaments and r-Transitive Feedback Arc Set In Tournaments admit linear vertex-kernels. Finally, we consider another generalization of Feedback Arc Set in Tournaments, which does not fit the aforementioned framework. We obtain a constant-factor approximation and a linear vertex-kernel for this problem.