Polyhedral Methods in Design Theory
This chapter is devoted to the relation between polyhedral theory and combinatorial designs. The polyhedral aspects of constructing packings, coverings and t-designs are emphasized. Classical results and algorithms in polyhedral theory are summarized, integer programming formulation of design construction problems are presented, and polyhedra associated to these formulations and related algorithms are discussed.
KeywordsValid Inequality Integer Programming Problem Integer Programming Formulation Incidence Vector Clique Inequality
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- D. Applegate, R. Bixby, V. Chvátal and W. Cook, Finding cuts in the TSP, preliminary report, August 1994.Google Scholar
- A. Bachem and M. Grötschel, New aspects of polyhedral theory, in Modern Applied Mathematics, Optimization and Operations Research, North-Holland Publishing Company, 1982, 51–106.Google Scholar
- V. Chvátal, On certain polytopes associated with graphs, Journal of Combinatorial Theory(B) 18(1975),138–154.Google Scholar
- C.D. Godsil, Linear algebra and designs, preprint, 1994.Google Scholar
- J.K. Lenstra AND A.H.G. Rinnooy Kan, Complexity of packing, covering and partitioning, in Packing and Covering in Combinatorics, A. Schrijver, ed., Mathematical Centre Trats 106, 1979, 275–291.Google Scholar
- W.H. Mills and R.C. Mullin, Coverings and Packings, in Contemporary Design Theory: a collection of surveys, J.H. Dinitz and D.R. Stinson, eds., Wiley, 1992, 371–399.Google Scholar
- G.L. Nemhauser and L.A. Wolsey, Integer and Combinatorial Optimization, John Wiley & Sons, 1988, 83–113.Google Scholar
- W.R. Pulleyblank, Polyhedral Combinatorics, in Handbooks in OR & MS, vol.1, N.L. Nemhauser et al., eds., North-Holland, 1989, 371–446.Google Scholar
- A. Schrijver, On cutting planes, in Combinatorics 79 Part II, Annals of Discrete Mathematics 9(1980), 291–296.Google Scholar
- R.M. Wilson, On the theory of t-designs, in Enumeration and Designs, D.M. Jackson and S.A. Vanstone, eds., Academic Press, Toronto, 1984, 19–49.Google Scholar