Faster algorithms for feedback arc set tournament, Kemeny rank aggregation and betweenness tournament

Abstract

We study fixed parameter algorithms for three problems: Kemeny rank aggregation, feedback arc set tournament, and betweenness tournament. For Kemeny rank aggregation we give an algorithm with runtime O*(2 O(√OPT)), where n is the number of candidates, OPT ≤ ( n2) is the cost of the optimal ranking, and O*(•) hides polynomial factors. This is a dramatic improvement on the previously best known runtime of O*(2O(OPT)). For feedback arc set tournament we give an algorithm with runtime O*(2 O(√OPT)), an improvement on the previously best known O*(OPTO(√OPT)) [4]. For betweenness tournament we give an algorithm with runtime O*(2O(√OPT/n)), where n is the number of vertices and OPT ≤ (n3) is the optimal cost. This improves on the previously known O*(OPTO(OPT1/3)) [28], especially when OPT is small. Unusually we can solve instances with OPT as large as n (log n)2 in polynomial time! © 2010 Springer-Verlag.