Blocking Polyhedra
ResearchPublished 1968
A geometric theory of "blocking polyhedra" is developed and applied to a number of problems in extremal combinatorics. The basic notion is a variant of the concept of polar polyhedra and exhibits a similar duality. The max-flow min-cut equality and the length-width inequality, valid for paths and cuts in a network, always hold for a blocking pair of polyhedra, and the former of these characterizes the blocking relation. A typical combinatorial application is a new geometric characterization of the permutation matrices as the extreme points of a certain unbounded convex polyhedron.
Document Details
- Copyright: RAND Corporation
- Availability: Web Only
- Year: 1968
- Pages: 33
- DOI: https://doi.org/10.7249/RM5834
- Document Number: RM-5834-PR
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