Approximation algorithms for integer covering problems via greedy column generation

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1. 1. V. CHVÁTAL, A greedy heuristic for the set-covering problem, Mathematics of Operations Research, 1979, 4, p. 233-235. Zbl0443.90066MR539404
2. 2. V. CHVÁTAL, Linear Programming, Freeman, New York, 1983. Zbl0537.90067MR717219
3. 3. H. DYCKHOFF, A typology of cutting and packing problems, European Journal of Operational Research, 1990, 44, p. 145-159. Zbl0684.90076MR1036150
4. 4. G. DOBSON, Worst-case analysis of greedy heuristics for integer programming with nonnegative data, Mathematics of Operations Research, 1982, 7, p. 515-531. Zbl0498.90061MR686528
5. 5. P. C. GILMORE, R. E. GOMORY, A linear programming approach to the cutting stock problem, Operations Research, 1963, 9, p. 849-859. Zbl0096.35501MR137589
6. 6. M. X. GOEMANS, D. P. WILLIAMSON, new 3/4-approximation algorithm for MAX SAT, In Proc. of the third IPCO Conference, G. RINALDI and L. WOLSEY eds., 1993, p. 313-321. Zbl0929.90071
7. 7. R. W. HAESSLER, P. E. SWEENEY, Cutting stock problems and solution procedures, European Journal of Operational Research, 1991, 54, p. 141-150. Zbl0736.90062
8. 8. P. HANSEN, B. JAUMARD, M. POGGI DE ARAGÃO, Column generation methods for probabilistic logic, ORSA Journal on Computing, 1991, 3, p. 135-148. Zbl0800.68864
9. 9. D. S. JOHNSON, Approximation algorithms for combinatorial problems, Journal of Computer and System Sciences, 1974, 9, p. 256-278. Zbl0296.65036MR449012
10. 10. D. S. JOHNSON, Worst-case behavior of graph coloring algorithms, In Proc. 5th Southeastern Conf. on Combinatorics, Graph Theory and Computing, p. 513-527. Utilitas Mathematica Publ. Winnipeg, Ontario, 1974 b. Zbl0308.05109MR389644
11. 11. D. KAVVADIAS, C. P. PAPADIMITRIOU, A linear programming approach to reasoning about probabilities, Annals of Mathematics and Artificial Intelligence, 1990, 1, p. 189-205. Zbl0878.68034
12. 12. L. LOVÁSZ, On the ratio of optimal integral and fractional covers, Discrete Mathematics, 1974, 13, p. 383-390. Zbl0323.05127MR384578
13. 13. C. LUND, M. YANNAKAKIS, On the hardness of approximating minimization problems, Working Paper AT&T Bell Labs, NJ, 1992. Zbl0814.68064
14. 14. M. MINOUX, A class of combinatorial problems with polynomially solvable large scale set covering/partioning relaxations, R.A.I.R.O. Recherche opérationnelle/Operations Research, 1987, 21, p. 105-136. Zbl0644.90061MR897292
15. 15. G. M. NEMHAUSER, L. A. WOLSEY, Integer and Combinatorial Optimization, Wiley- Interscience Series in Discrete Mathematics and Optimization, John Wiley & Sons, New York Chichester Brisbane Toronto Singapore, 1988. Zbl0944.90001MR948455
16. 16. N. J. NILSSON, Probabilistic logic, Artificial Intelligence, 1986, 28, p. 71-87. Zbl0589.03007MR832294
17. 17. H. U. SIMON, The analysis of dynamic and hybrid channel assignment, Working Paper, Universität des Saarlandes, Saarbrücken, 1988. 
18. 18. H. U. SIMON, On approximate solutions for combinatorial optimization problems, SIAM Journal on Discrete Mathematics, 1990, 3, p. 294-310. Zbl0699.68077MR1039300

1. Nelson Maculan, Marcos de Mendonça Passini, José André de Moura Brito, Irene Loiseau, Column-generation in integer linear programming
2. Nelson Maculan, Marcos de Mendonça Passini, José André de Moura Brito, Irene Loiseau, Column-Generation in Integer Linear Programming