Meeks, K. (2016) Randomised Enumeration of Small Witnesses Using a Decision Oracle. In: 11th International Symposium on Parameterized and Exact Computation (IPEC 2016), Aarhus, Denmark, 24-26 Aug 2016, ISBN 9783959770231 (doi: 10.4230/LIPIcs.IPEC.2016.22)
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Publisher's URL: http://drops.dagstuhl.de/opus/volltexte/2017/6921/
Abstract
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.
Item Type: | Conference Proceedings |
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Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Meeks, Dr Kitty |
Authors: | Meeks, K. |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
ISSN: | 1868-8969 |
ISBN: | 9783959770231 |
Copyright Holders: | Copyright © 2016 Kitty Meeks |
Publisher Policy: | Reproduced under a Creative Commons License |
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