In this paper we carry out a systematic study of a natural covering problem, used for identification across several areas, in the realm of parameterized complexity. In the Test Cover problem we are given a set [n] = {1,...,n} of items together with a collection, , of distinct subsets of these items called tests. We assume that is a test cover, i.e., for each pair of items there is a test in containing exactly one of these items. The objective is to find a minimum size subcollection of , which is still a test cover. The generic parameterized version of Test Cover is denoted by -Test Cover. Here, we are given and a positive integer parameter k as input and the objective is to decide whether there is a test cover of size at most . We study four parameterizations for Test Cover and obtain the following: (a) k-Test Cover, and (n - k)-Test Cover are fixed-parameter tractable (FPT), i.e., these problems can be solved by algorithms of runtime , where f(k) is a function of k only. (b) -Test Cover and (logn + k)-Test Cover are W[1]-hard. Thus, it is unlikely that these problems are FPT. © 2012 Springer-Verlag.
CITATION STYLE
Crowston, R., Gutin, G., Jones, M., Saurabh, S., & Yeo, A. (2012). Parameterized study of the test cover problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7464 LNCS, pp. 283–295). https://doi.org/10.1007/978-3-642-32589-2_27
Mendeley helps you to discover research relevant for your work.