INCIDENCE MATRICES WITH THE CONSECUTIVE 1'S PROPERTY

Abstract

Let A = (aij) be an m-by-n matrix whose entries aij are all either 0 or 1. For certain applications it is of interest to know whether or not there is an m-by-m permutation matrix P such that the 1's in each column of PA occur in consecutive positions. In this note certain results having relevance to this problem are stated. Proofs of these results together with computationally effective algorithms for deciding the question are to be published elsewhere. The problem formulated above is directly related to that of determining whether a given finite, undirected graph is an interval graph. Although necessary and sufficient conditions are known for the solution of this latter problem, the approach used here is quite different from those used heretofore and seems to lead to highly efficient algorithms not only for resolving the question, but also for producing a representative set of intervals in the affirmative case.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1964
Accession Number
AD0650430

Entities

People

  • D. R. Fulkerson
  • O. A. Gross

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Computational Science
  • Decomposition
  • Genetic Structures
  • Inequalities
  • Intervals
  • Mathematics
  • Permutations
  • Standards
  • United States

Fields of Study

  • Mathematics

Readers

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