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

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 √ ), where n is the number of candidates, OPT ≤ ( 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(2 ). For feedback arc set tournament we give an algorithm with runtime O(2 √ OPT ), an improvement on the previously best known O(OPT √ OPT ) Alon et al. [2009]. For betweenness tournament we give an algorithm with runtime O(2 √ ), where n is the number of vertices and OPT ≤ ( n 3 ) is the optimal cost. This improves on the previously known O(OPT ) Saurabh [2009]), especially when OPT is small. Unusually we can solve instances with OPT as large as n(log n) in polynomial time!