Branch-and-Bound Algorithms for the Test Cover Problem

Authors:
Koen M. J. De Bontridder;B. J. Lageweg;Jan K. Lenstra;James B. Orlin;Leen Stougie
Affiliations:
-;-;-;-;-
Venue:
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Year:
2002

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Abstract

In the test cover problem a set of items is given together with a collection of subsets of the items, called tests. A smallest subcollection of tests is to be selected such that for every pair of items there is a test in the selection that contains exactly one of the two items. This problem is NP-hard in general. It has important applications in biology, pharmacy, and the medical sciences, as well as in coding theory.We develop a variety of branch-and-bound algorithms to solve the problem to optimality. The variety is in the definition of the branching rules and the lower bounds to prune the search tree. Our algorithms are compared both theoretically and empirically.