文章基本信息

标题：Randomised Enumeration of Small Witnesses Using a Decision Oracle
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作者：Kitty Meeks
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2016
卷号：63
页码：22:1-22:12
DOI：10.4230/LIPIcs.IPEC.2016.22
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：Many combinatorial problems involve determining whether a universe of n elements contains a witness consisting of k elements which have some specified property. In this paper we investigate the relationship between the decision and enumeration versions of such problems: efficient methods are known for transforming a decision algorithm into a search procedure that finds a single witness, but even finding a second witness is not so straightforward in general. In this paper we show that, if the decision version of the problem belongs to FPT, there is a randomised algorithm which enumerates all witnesses in time f(k)*poly(n)*N, where N is the total number of witnesses and f is a computable function. This also gives rise to an efficient algorithm to count the total number of witnesses when this number is small.
关键词：enumeration algorithms; parameterized complexity; randomized algorithms; color coding