Abstract
One form of the integer 1.p. problem is to (1) find integers x = (xj: j ∈ J) such that (2) x ≥ 0, Ax ≤ b, and (3) cx is maximum, where A = (aij: i ∈ I, j ∈ J), b = (bi: i ∈ I), and c = (cj: j ∈ J) are given integers. Usually some condition holds on A, b, and c which makes it obvious that there is a finite algorithm — let us say that (4) x ≤ d for every x of (2).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aroaz, J. Polyhedral Neopolarities, Thesis, Univ. of Waterloo, 1974.
Cunningham, W., A Combinatorial Decomposition Theory, Thesis, University of Waterloo, 1974.
Chvatal, V., Edmonds Polyedra and a Hierarchy of Combinatorial Problems.
Giles, R., and Edmonds, J., Supermodular Functions and Combinatorial Polyhedra, Report, University of Waterloo.
Edmonds, J., Maximum Matching and Polyhedron with 0, 1 Vertices
—, Johnson, E., Lockhart, S., Blossom I, A computer code for the Matching Problem.
—, Submodular functions, Matroids, and Certain Polyhedra, Comb. Structures and their applic.
—, Matroid Intersection, Report, University of Waterloo
—, Matroid Partition, Mathematics of the decision sciences, G.B.Dantzig and A.F.Veinott editors.
—, Edge-disjoint branchings, Combinatorial Algorithms, R. Rustin (ed.), Algorithmics Press, New York, 1972.
—, and Pulleyblank, W., Optimum Matching Theory, to appear, Johns Hopkins Press.
Jenkyns, T., Matchoids: A Generalization of Matchings and Matroids, Thesis, University of Waterloo, 1974.
Lovasz, L., “On Two Theorems in Graph Theory”, to appear.
Tarjan, R., “A Good Algorithm for Edge-Disjoint Branchings”, to appear.
Pulleyblank, W., The Faces of Matching Polyhedra, Thesis, University of Waterloo, 1974
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1975 D. Reidel Publishing Company, Dordrecht-Holland
About this paper
Cite this paper
Edmonds, J. (1975). Some Well-Solved Problems in Combinatorial Optimization. In: Roy, B. (eds) Combinatorial Programming: Methods and Applications. NATO Advanced Study Institutes Series, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-7557-9_15
Download citation
DOI: https://doi.org/10.1007/978-94-011-7557-9_15
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-011-7559-3
Online ISBN: 978-94-011-7557-9
eBook Packages: Springer Book Archive