Randomised Enumeration of Small Witnesses Using a Decision Oracle

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, (doi:10.4230/LIPIcs.IPEC.2016.22)

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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
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
Copyright Holders:Copyright © 2016 Kitty Meeks
Publisher Policy:Reproduced under a Creative Commons License
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