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(sqrt{OPT})), where n is the number of candidates, OPT 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*(2^O(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})) (Alon, Lokshtanov and Saurabh 2009). For betweenness tournament we give an algorithm with runtime O*(2^O(sqrt{OPT/n})), where n is the number of vertices and OPT is the optimal cost. This improves on the previously known O*(OPT^O(OPT^{1/3}))$ (Saurabh 2009), especially when OPT is small. Unusually we can solve instances with OPT as large as n (log n)^2 in polynomial time!
Cite
@article{arxiv.1006.4396,
title = {Faster Algorithms for Feedback Arc Set Tournament, Kemeny Rank Aggregation and Betweenness Tournament},
author = {Marek Karpinski and Warren Schudy},
journal= {arXiv preprint arXiv:1006.4396},
year = {2010}
}
Comments
14 pages. Version 1 of arXiv:0911.2214 includes a preliminary version of this work; version 2 does not