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

Ontology type: schema:Chapter      Open Access: True

Chapter Info

DATE

2010

AUTHORS 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$O^*(2^{O(\sqrt{OPT})})$\end{document}, where n is the number of candidates, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$OPT \le \binom{n}{2}$\end{document} 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$O^*(2^{O(\sqrt{OPT})})$\end{document}, an improvement on the previously best known \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$O^*(OPT^{O(\sqrt{OPT})})$\end{document} [4]. For betweenness tournament we give an algorithm with runtime \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$O^*(2^{O(\sqrt{OPT/n})})$\end{document}, where n is the number of vertices and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$OPT \le \binom{n}{3}$\end{document} is the optimal cost. This improves on the previously known \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$O^*(OPT^{O(OPT^{1/3})})$\end{document} [28], especially when OPT is small. Unusually we can solve instances with OPT as large as n (logn)2 in polynomial time! More... »

PAGES

3-14

Book

TITLE

Algorithms and Computation

ISBN

978-3-642-17516-9
978-3-642-17517-6

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-642-17517-6_3

DOI

http://dx.doi.org/10.1007/978-3-642-17517-6_3

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