Computational experience with approximation algorithms for the set covering problem

European Journal of Operational Research

Volumn 101, Issue 1, 1997, Pages 81-92

  Grossman, Tal ^a   Wool, Avishai ^b,c  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^c LUCENT TECHNOLOGIES   (United States)

Author keywords

Approximation algorithms; Neural networks; Optimization; Set covering

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL METHODS; NEURAL NETWORKS; OPTIMIZATION; SET THEORY;

APPROXIMATION ALGORITHMS;

COMBINATORIAL MATHEMATICS;

EID: 0031199150     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-2217(96)00161-0     Document Type: Article

References (30)

1. Arora, S., Lund, C., Motwani, R., Sudan, M., and Szegedy, M. (1992), "Proof verification and hardness of approximating problems", in: Proceedings 33rd IEEE Symp. Found. of Comp. Science 14-23.
2. Balas, E., and Ho, A. (1980), "Set covering algorithms using cutting planes, heuristics, and subgradient optimization: a computational study", Math. Programming 12, 37-60.
3. Beasley, J.E. (1987), "An algorithm for set covering problem", Euro. J. Operational Research 31, 85-93.
4. Beasley, J.E. ( 1990), "A lagrangian heuristic for set covering problems", Naval Research Logistics 37, 151-164.
5. Beasley, J.E. (1990), "OR-library: Distributing test problems by electronic mail", J. Oper. Res. Soc. 41/11, 1069-1072. See also in WWW site http://mscmga.ms.ic.ac.uk/info.html.
6. Beasley, J.E., and Chu, P.C. (1996), "A genetic algorithm for the set covering problem". Euro. J. Operational Research 94, 392-404.
7. n", J. Graph Theory 19/1, 17-23.
8. Chvátal, V. ( 1979), "A greedy heuristic for the set-covering problem", Math. of Oper. Res. 4/3, 233-235.
9. Croall, I.F., and Mason, J.P., eds. (1991), Industrial Applications of Neural Networks, Springer-Verlag, Berlin.
10. Erdos, P. (1963), "On a combinatorial problem I", Nordisk Mat. Tidskrift 11, 5-10.
11. Erdos, P. (1990), "On some of my favorite problems in graph theory and block designs", Le Matematische 45, 61-74.
12. Feige, U. (1993), Personal communication.
13. Garey, M.R., and Johnson, D.S. (1979), Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco.
14. Gavril, F. (1974), appears in [13], p. 134.
15. Goldberg, M.K., and Russell, H.C. (1995), "Toward computing m(4)", Ars Combinatoria 3/9, 139-148.
16. Grossman, T. (1994), "A neural network algorithm for the minimum cover problem", unpublished manuscript.
17. Grossman, T., and Wool, A. (1994), "Computational experience with approximation algorithms for the set covering problem". Technical Report CS94-25, The Weizmann Institute of Science, Rehovot, Israel.
18. Harborth, H., and Nienborg, H. (1995), "Maximum number of edges in a six-cube without four-cycles" (to appear in Bull. Inst. Combin. Appl.).
19. Hochbaum, D.S. (1982), "Approximation algorithms for the set covering and vertex cover problems", SIAM J. Computing 11/3, 555-556.
20. Jefries, C. (1991), Code Recognition and Set Selection with Neural Networks, Birkhauser, Boston.
21. Johnson, D.S. (1974), "Approximation algorithms for combinatorial problems", J. Computer System Sci. 9, 256-278.
22. Lovász, L. (1975), "On the ratio of optimal integral and fractional covers", Disc. Math. 13, 383-390.
23. Papadimitriou, C.H., and Yannakakis, M. (1991), "Optimization, approximation, and complexity classes", J. Computer System Sci. 43, 425-440.
24. Peleg, D., Schechtman, G., and Wool, A. (1993), "Approximating bounded 0-1 integer linear programs", in: Proceedings 2nd Israel Symp. Theory of Computing Sys., Netanya, Israel, 69-77.
25. Peleg, D., Schechtman, G., and Wool, A. (1996), "Randomized approximation of bounded multicovering problems", Algorithmica (to appear).
26. Peng, Y., and Reggia, J.A. (1989), "A connectionist model for diagnostic problem solving", IEEE Transactions on Systems, Man, and Cybernetics 19, 285.
27. Sen, S. (1993), "Minimal cost set covering using probabilistic methods", in: Proceedings ACM Symp. Applied Computing, Indianapolis, 157-164.
28. Vanderbei, R.J. (1992), "LOQO user's manual", Program in Statistics & Operations Research, Princeton University, NJ.
29. Vercellis, C. (1984), "A probabilistic analysis of the set covering problem", Annals of Oper. Res. 1, 255-271.
30. Wedelin, D. (1994), "An algorithm for 0-1 programming with application to airline crew scheduling", in: Euro. Symp. Algorithms.