ISAAC 2010: Algorithms and Computation pp 3-14

Faster Algorithms for Feedback Arc Set Tournament, Kemeny Rank Aggregation and Betweenness Tournament

• Marek Karpinski
• Warren Schudy
Conference paper

DOI: 10.1007/978-3-642-17517-6_3

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6506)
Cite this paper as:
Karpinski M., Schudy W. (2010) Faster Algorithms for Feedback Arc Set Tournament, Kemeny Rank Aggregation and Betweenness Tournament. In: Cheong O., Chwa KY., Park K. (eds) Algorithms and Computation. ISAAC 2010. Lecture Notes in Computer Science, vol 6506. Springer, Berlin, Heidelberg

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 $$O^*(2^{O(\sqrt{OPT})})$$, where n is the number of candidates, $$OPT \le \binom{n}{2}$$ 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 $$O^*(2^{O(\sqrt{OPT})})$$, an improvement on the previously best known $$O^*(OPT^{O(\sqrt{OPT})})$$ [4]. For betweenness tournament we give an algorithm with runtime $$O^*(2^{O(\sqrt{OPT/n})})$$, where n is the number of vertices and $$OPT \le \binom{n}{3}$$ is the optimal cost. This improves on the previously known $$O^*(OPT^{O(OPT^{1/3})})$$ [28], especially when OPT is small. Unusually we can solve instances with OPT as large as n (logn)2 in polynomial time!

Keywords

Kemeny rank aggregation Feedback arc set tournament Fixed parameter tractability Betweenness tournament