NETWORKS, FRAMES, BLOCKING SYSTEMS
Abstract
A survey of some of the basic problems, theorems, and constructions for flow networks, and their extension to more general combinatorial structures. One generalization is that obtained by replacing the vertex-edge incidence matrix of an oriented network by an arbitrary real matrix. This leads to the notion of a frame of a sub-space of Euclidean n-space, a concept very closely allied to that of a real matric matroid. The treatment relates matroid theory and linear programming theory, and thus provides another viewpoint on linear programming, and in particular, on digraphoid-programming. In addition, a very general combinatorial structure called a blocking system is given an axiomatic formulation. These systems have arisen in a variety of contexts, including multi-person game theory and abstract covering problems. It is shown that one of the network theorems surveyed in the study extends to all blocking systems, and indeed characterizes such systems.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1967
- Accession Number
- AD0653178
Entities
People
- D. R. Fulkerson
Organizations
- RAND Corporation