A quadratic vertex kernel for feedback arc set in bipartite tournaments

Authors:
Mingyu Xiao;Jiong Guo
Affiliations:
School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, China;Universität des Saarlandes, Saarbrücken, Germany
Venue:
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Year:
2012

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Abstract

The k-feedback arc set problem is to determine whether there is a set F of at most k arcs in a directed graph G such that the removal of F makes G acyclic. The k-feedback arc set problems in tournaments and bipartite tournaments (k-FAST and k-FASBT) have applications in ranking aggregation and have been extensively studied from the viewpoint of parameterized complexity. Recently, Misra et al. provide a problem kernel with O(k3) vertices for k-FASBT. Answering an open question by Misra et al., we improve the kernel bound to O(k2) vertices by introducing a new concept called "bimodule."