Abstract
A small but notoriously hard integer program formulated by Donald Knuth fifty years ago is solved by three versions of a lexicographic algorithm using Gomory cuts. The lexicographic cutting plane algorithms are faster than CPLEX on this problem by a factor of at least 10.
This is a preview of subscription content, log in via an institution to check access.
References
Balas E., Fischetti M., Zanette A.: On the enumerative nature of Gomory’s dual cutting plane method. Math. Program. Ser. B 125, 325–351 (2010)
Knuth D.: Minimizing drum latency time. J. ACM 8, 119–150 (1961)
Knuth, D.: An integer programming problem. Manuscr. July (1993)
Knuth, D.: Selected Papers on Design of Algorithms, pp. 435–436. CSLI Lecture Notes no. 191, Stanford, California, February (2010)
Zanette, A., Fischetti, M., Balas, E.: Lexicography and degeneracy: can a pure cutting plane algorithm work? Math. Program. Ser. A (2009). doi:10.1007/s10107-009-0335-0
Author information
Authors and Affiliations
Corresponding author
Additional information
This note is an Addendum to [5].
Rights and permissions
About this article
Cite this article
Balas, E., Fischetti, M. & Zanette, A. A hard integer program made easy by lexicography. Math. Program. 135, 509–514 (2012). https://doi.org/10.1007/s10107-011-0450-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10107-011-0450-6
Keywords
- Cutting plane methods
- Gomory cuts
- Degeneracy in linear programming
- Lexicographic dual simplex
- Computational analysis