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On the facial structure of set packing polyhedra.(English)Zbl 0272.90041


MSC:

90C10 Integer programming

Cite

References:

[1]J.P. Arabeyre, J. Fearnley, F. Steiger and W. Teather, ”The airline crew scheduling problem: A survey”,Transportation Science 3 (1969) 140–163. ·doi:10.1287/trsc.3.2.140
[2]E. Balas and M.W. Padberg, ”On the set covering problem”,Operations Research 20 (1972) 1152–1161. ·Zbl 0254.90035 ·doi:10.1287/opre.20.6.1152
[3]E. Balas and M.W. Padberg, ”On the set covering problem II: An algorithm”, Management Sciences Research Report No. 278, GSIA, Carnegie–Mellon University, Pittsburgh, Pa. (presented at the Joint National Meeting of ORSA, TIMS, AIEE, at Atlantic City, November 8–10, 1972). ·Zbl 0254.90035
[4]M.L. Balinski, ”On recent developments in integer programming”, in:Proceedings of the Princeton Symposium on Mathematical Programming, Ed. H.W. Kuhn (Princeton University Press, Princeton, N.J., 1970). ·Zbl 0222.90036
[5]M.L. Balinski, ”On maximum matching, minimum covering and their connections”, in:Proceedings of the Princeton Symposium on Mathematical Programming, Ed. H.W. Kuhn (Princeton University Press, Princeton, N.J., 1970). ·Zbl 0228.05122
[6]L.W. Beineke, ”A Survey of packings and coverings of graphs”, in:The many facets of graph theory, Eds. G. Chartrand and S.F. Kapoor (Springer, Berlin, 1969). ·Zbl 0186.27601
[7]J.Edmonds, ”Covers and packings in a family of sets”,Bulletin of the American Mathematical Society 68 (1962) 494–499. ·Zbl 0106.24201 ·doi:10.1090/S0002-9904-1962-10791-5
[8]J. Edmonds, ”Maximum matching and a polyhedron with 0, 1 vertices”,Journal of Research of the National Bureau of Standards 69B (1965) 125–130. ·Zbl 0141.21802
[9]D.R. Fulkerson, ”Blocking and anti-blocking pairs of polyhedra”,Mathematical Programming 1 (1971) 168–194. ·Zbl 0254.90054 ·doi:10.1007/BF01584085
[10]R. Garfinkel and G.L. Nemhauser, ”The set-partitioning problem: Set covering with equality constraints”,Operations Research 17 (1969) 848–856. ·Zbl 0184.23101 ·doi:10.1287/opre.17.5.848
[11]R.S. Garfinkel and G.L. Nemhauser, ”A survey of integer programming emphasizing computation and relations among models”, Technical Report No. 156, Department of Operations Research, Cornell University, Ithaca, N.Y. (1972). ·Zbl 0271.90028
[12]R.E. Gomory, ”Some polyhedra connected with combinatorial problems”,Linear Algebra 2 (1969) 451–558. ·Zbl 0184.23103 ·doi:10.1016/0024-3795(69)90017-2
[13]D.K. Guha, ”Set covering problem with equality constraints”, The Port of New York Authority, New York (1970).
[14]F. Harary,Graph Theory (Addison–Wesley, Reading, Mass., 1969).
[15]F. Harary and I.C. Ross, ”A procedure for clique detection using the group matrix”,Sociometry 20 (1957) 205–215. ·doi:10.2307/2785673
[16]R.M. Karp, ”Reducibility and combinatorial problems”, Technical Report 3, Department of Computer Science, University of California, Berkeley, Calif. (1972). ·Zbl 0366.68041
[17]J. Messier and P. Robert, ”Recherche des cliques d’un graphe irreflexif fini”, Publication No. 73, Departement d’Informatique, Université de Montréal (Novembre 1971).
[18]O. Ore,Theory of graphs, American Mathematical Society Colloquium Publications 38 (American Mathematical Society, Providence, R.I., 1962). ·Zbl 0105.35401
[19]M.W. Padberg, Essays in integer programming, Ph. D. Thesis, Carnegie–Mellon University, Pittsburgh, Pa. (April 1971), unpublished.
[20]M.W. Padberg, ”On the facial structure of set covering problems”, IIM Preprint No. I/72-13, International Institute of Management, Berlin (1972), (presented at the 41st National Meeting of ORSA, New Orleans, La., April 26–28, 1972).
[21]J.F. Pierce, ”Application of combinatorial programming to a class of all-zero–one integer programming problems”,Management Science 15 (1968) 191–212. ·doi:10.1287/mnsc.15.3.191
[22]H. Thiriez, Airline crew scheduling, a group theoretic approach, Ph. D. Thesis, Massachusetts Institute of Technology, Cambridge, Mass., FTL-R69-1 (1969) (published in RIRO 5 (1971) 83–103). ·Zbl 0266.90039
[23]V.A. Trubin, ”On a method of solution of integer linear programming problems of a special kind”,Soviet Mathematics Doklady 10 (1969) 1544–1546. ·Zbl 0209.51201
[24]L.A. Wolsey, ”Extensions of the group theoretic approach in integer programming”,Management Science 18 (1971) 74–83. ·Zbl 0239.90034 ·doi:10.1287/mnsc.18.1.74
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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