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Faces for a linear inequality in O-1 variables.(English)Zbl 0314.90063


MSC:

90C10 Integer programming
52C17 Packing and covering in \(n\) dimensions (aspects of discrete geometry)
05B35 Combinatorial aspects of matroids and geometric lattices

Cite

References:

[1]E. Balas and R. Jeroslow, ”Canonical cuts on the unit hypercube”,SIAM Journal on Applied Mathematics 23 (1) (1972) 61–69. ·Zbl 0237.52004 ·doi:10.1137/0123007
[2]E. Balas, ”Facets of the knapsack polytope”,Mathematical Programming 8 (1975) 146–164 (this issue). ·Zbl 0316.90046 ·doi:10.1007/BF01580440
[3]G.H. Bradley, P.L. Hammer and L.A. Wolsey, ”Coefficient reduction for inequalities in 0–1 variables”,Mathematical Programming 7 (1974) 263–282. ·Zbl 0292.90038 ·doi:10.1007/BF01585527
[4]V. Chvatal, ”On certain polytopes associated with graphs”, Tech. Rept. CRM-238, Université de Montréal (1970). ·Zbl 0226.05106
[5]V. Chvatal and P.L. Hammer, ”Set packing problems and threshold graphs”, Centre de Recherches Mathématiques, Université de Montréal (August 1973).
[6]J. Edmonds, ”Matroids and the Greedy Algorithm”,Mathematical Programming 1 (1971) 127–136. ·Zbl 0253.90027 ·doi:10.1007/BF01584082
[7]J. Edmonds, ”Maximum matching and a polyhedron with 0–1 vertices”,Journal of Research of the National Bureau of Standards 6913 (1965) 125–130. ·Zbl 0141.21802
[8]J. Edmonds, ”Submodular functions, matroids and certain polyhedra”, in: H. Guy, ed.,Combinatorial structures and their applications (Gordon and Breach, New York, 1969). ·Zbl 0268.05019
[9]F. Glover, ”Unit coefficient inequalities for zero–one programming”, Management Science Report Series No. 73-7, University of Colorado (July 1973).
[10]B. Grünbaum,Convex polytopes (Wiley, New York, 1967). ·Zbl 0163.16603
[11]P.L. Hammer, E.L. Johnson and U.N. Peled, ”Regular 0–1 programs”, Research Rept. CORR No. 73-19, University of Waterloo (September 1973). ·Zbl 0304.90081
[12]P.L. Hammer, E.L. Johnson and U.N. Peled, ”Facets of regular 0–1 polytopes”,Mathematical Programming 8 (1975) 179–206 (this issue). ·Zbl 0314.90064 ·doi:10.1007/BF01580442
[13]G.L. Nemhauser and L.E. Trotter, Jr., ”Properties of vertex packing and independence systems polyhedra”,Mathematical Programming 6 (1974) 48–61. ·Zbl 0281.90072 ·doi:10.1007/BF01580222
[14]M.W. Padberg, ”On the facial structure of set covering problems”, Reprint Series of the International Institute of Management, Berlin (April 1972).
[15]M.W. Padberg, ”A note on 0–1 programming”, Reprint 173/24, International Institute of Management, Berlin (March 1973).
[16]L.E. Trotter, Jr., ”Solution characteristics and algorithms for the vertex packing problem”, Tech. Rept. No. 168, Dept. of Operations Research, Cornell University (January 1973).
[17]L.A. Wolsey, ”An algorithm to determine optimal equivalent inequalities in 0–1 variables”, IBM Symposium on Discrete Optimization, Wildbad, Germany, October 1972.
[18]L.A. Wolsey, ”Faces for linear inequalities in 0–1 variables”, Mimeo, Louvain (July 1973).
[19]L.A. Wolsey, ”Faces for linear inequalities in 0–1 variables”, CORE Discussion Paper No. 7338, Louvain (November 1973).
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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