MULTI-COMMODITY NETWORK SOLUTIONS.

Abstract

Multicommodity network flow problems have rational optimal solutions, in general, because the constraint matrix is not unimodular. Thus, all algorithms proposed to date require solving the equivalent of a general linear program in order to allocate the mutual capacities correctly, and it is here that fractional solutions may arise. This paper attempts to characterize the nature of these rational solutions by presenting several conjectures about the 'modularity' of multicommodity flow problems. Fundamental differences between the directed- and undirected-arc case are revealed, as well as the important role played by individual capacity constraints. Further investigations seems to require the development of new combinatorial and graph-theoretic methods. (Author)

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1966
Accession Number
AD0639672

Entities

People

  • William S. Jewell

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Commodities
  • Computational Complexity
  • Computations
  • Evolutionary Algorithms
  • Graph Theory
  • Heuristic Methods
  • Linear Programming
  • Mathematical Analysis
  • Mathematics
  • Simplex Method

Readers

  • Graph Algorithms and Convex Optimization.
  • Systems Analysis and Design