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 de.nition of the branching rules and the lower bounds to prune the search tree. Our algorithms are compared both theoretically and empirically.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H.Y. Chang, E. Manning, G. Metze, Fault diagnosis of digital systems, Wiley, New York, 1970.
K.M. J. DeBontridder, Methods for solving the test cover problem, Master’s Thesis, Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, February 1997.
K.M. J. De Bontridder, B.V. Halldórsson, M. M. Halldórsson, C.A. J. Hurkens, J.K. Lenstra, R. Ravi, L. Stougie, Approximation algorithms for the test cover problem, Submitted for publication, 2002.
M.R. Garey, D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-completeness, Freeman, San Francisco, 1979.
A.W. J. Kolen, J.K. Lenstra, Combinatorics in operations research, in R. Graham, M. Grötschel, L. Lovász (eds.), Handbook of Combinatorics, Elsevier, Amsterdam, 1995, 1875–1910.
B. J. Lageweg, J.K. Lenstra, A.H. G. Rinnooy Kan, Uit de practijk van de besliskunde, In A.K. Lenstra, H.W. Lenstra, J.K. Lenstra, editors, Tamelijk briljant; Opstellen aangeboden aan Dr. T. J. Wansbeek. Amsterdam, 1980.
B.M. E. Moret, Decision trees and diagrams, Computing Surveys 14, 1982, 593–623.
B.M. E. Moret, H. D. Shapiro, On minimizing a set of tests. SIAM Journal on Scientific and Statistical Computing 6, 1985, 983–1003.
R.W. Payne, Selection criteria for the construction of e.cient diagnostic keys. Journal of Statistical Planning and Information 5, 1981, 27–36.
A. Rescigno, G.A. Maccacaro, The information content of biological classification, in C. Cherry (ed.), Information Theory: Fourth London Symposium, Butterworths, London, 1961, 437–445.
E. W. Rypka, W.E. Clapper, I.G. Brown, R. Babb, A model for the identi.cation of bacteria. Journal of General Microbiology 46, 1967, 407–424.
E. W. Rypka, L. Volkman, E. Kinter, Construction and use of an optimized identification scheme. Laboratory Magazine 9, 1978, 32–41.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
De Bontridder, K.M.J., Lageweg, B.J., Lenstra, J.K., Orlin, J.B., Stougie, L. (2002). Branch-and-Bound Algorithms for the Test Cover Problem. In: Möhring, R., Raman, R. (eds) Algorithms — ESA 2002. ESA 2002. Lecture Notes in Computer Science, vol 2461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45749-6_23
Download citation
DOI: https://doi.org/10.1007/3-540-45749-6_23
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44180-9
Online ISBN: 978-3-540-45749-7
eBook Packages: Springer Book Archive