An Improved Branch-and-Bound Algorithm for the Test Cover Problem

  • Torsten Fahle
  • Karsten Tiemann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3503)


The test cover problem asks for the minimal number of tests needed to uniquely identify a disease, infection, etc. At ESA’02 a collection of branch-and-bound algorithms was proposed by [4]. Based on their work, we introduce several improvements that are compatible with all techniques described in [4]. We present a faster data structure, cost based variable fixing and adapt an upper bound heuristic. The resulting algorithm solves benchmark instances up to 10 times faster than the former approach and up to 100 times faster than a general MIP-solver.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Beasley, J.E.: A Lagrangian Heuristic for Set-Covering Problems. Naval Research Logistics 37, 151–164 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Caprara, A., Fischetti, M., Toth, P.: Algorithms for the Set Covering Problem. Annals of Operations Research 98, 353–371 (2001)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Garey, M.R., Johnson, D.S.: Computers and Intractability. W.H. Freeman and Co, New York (1979)zbMATHGoogle Scholar
  4. 4.
    De Bontridder, K.M.J., Lageweg, B.J., Lenstra, J.K., Orlin, J.B., Stougie, L.: Branch-and-Bound Algorithms for the Test Cover Problem. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 223–233. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  5. 5.
    Halldórsson, B.V., Halldórsson, M.M., Ravi, R.: On the Approximability of the Minimum Test Collection Problem. In: Meyer auf der Heide, F. (ed.) ESA 2001. LNCS, vol. 2161, pp. 158–169. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. 6.
    Held, M., Karp, R.M.: The Traveling-Salesman Problem and Minimum Spanning Trees: Part II. Mathematical Programming 1, 6–25 (1971)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Moret, B., Shapiro, H.: On Minimizing a Set of Tests. SIAM Journal on Scientific and Statistical Computing 6, 983–1003 (1985)CrossRefGoogle Scholar
  8. 8.
    Payne, R.W.: Selection Criteria for the Construction of Efficient Diagnostic Keys. Journal of Statistical Planning and Information 5, 27–36 (1981)CrossRefGoogle Scholar
  9. 9.
    Rypka, E.W., Clapper, W.E., Brown, I.G., Babb, R.: A Model for the Identification of Bacteria. Journal of General Microbiology 46, 407–424 (1967)Google Scholar
  10. 10.
    Rypka, E.W., Volkman, L., Kinter, E.: Construction and Use of an Optimized Identification Scheme. Laboratory Magazine 9, 32–41 (1978)Google Scholar
  11. 11.
    K. Tiemann. Ein erweiterter Branch-and-Bound-Algorithmus für das Test-Cover Problem. Bachelor-Thesis (in German), University of Paderborn (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Torsten Fahle
    • 1
  • Karsten Tiemann
    • 1
  1. 1.Faculty of Computer Science, Electrical Engineering and MathematicsUniversity of PaderbornPaderbornGermany

Personalised recommendations