Abstract
We consider ternary matrices, i.e., integer matrices having all entries 0, 1 or 2. Three associated problems—the group problem, covering, and packing—are studied. General classes of vertices and facets are discussed in each case. Certain lifting procedures are also described. For all three problems techniques used are natural extensions of those used in the binary case.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. Chopra, D.L. Jensen and E.L. Johnson, “Polyhedra of regularp-nary group problems,”Mathematical Programming 43 (1989) 1–29.
D.R. Fulkerson, “Blocking polyhedra,” in: B. Harris, ed.,Graph Theory and its Applications (Academic Press, New York, 1970) pp. 93–112.
R.E. Gomory, “Some polyhedra related to combinatorial problems,”Journal of Linear Algebra and its Applications 2 (1969) 451–558.
G.L. Nemhauser and L.E. Trotter, Jr., “Properties of vertex packing and independence system polyhedra,”Mathematical Programming 6 (1974) 48–61.
M.W. Padberg, “On the facial structure of set packing polyhedra,”Mathematical Programming 5 (1973) 199–215.
M.W. Padberg, “A note on 0–1 programming,”Operations Research 23 (1975) 833–837.
L.E. Trotter, “A class of facet producing graphs for vertex Packing polyhedra,”Discrete Mathematics 12 (1975) 373–388.