文章基本信息

标题：A Polynomial-Time Randomized Reduction from Tournament Isomorphism to Tournament Asymmetry
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作者：Pascal Schweitzer
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2017
卷号：80
页码：66:1-66:14
DOI：10.4230/LIPIcs.ICALP.2017.66
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：The paper develops a new technique to extract a characteristic subset from a random source that repeatedly samples from a set of elements. Here a characteristic subset is a set that when containing an element contains all elements that have the same probability. With this technique at hand the paper looks at the special case of the tournament isomorphism problem that stands in the way towards a polynomial-time algorithm for the graph isomorphism problem. Noting that there is a reduction from the automorphism (asymmetry) problem to the isomorphism problem, a reduction in the other direction is nevertheless not known and remains a thorny open problem. Applying the new technique, we develop a randomized polynomial-time Turing-reduction from the tournament isomorphism problem to the tournament automorphism problem. This is the first such reduction for any kind of combinatorial object not known to have a polynomial-time solvable isomorphism problem.
关键词：graph isomorphism; asymmetry; tournaments; randomized reductions