Finding Minimum-Cost Circulations by Canceling Negative Cycles,

Abstract

A classical algorithm for finding a minimum-cost circulation consists of repeatedly finding a residual cycle of negative cost and canceling it by pushing enough flow around the cycle to saturate an arc. We show that a judicious choice of cycles for canceling leads to a polynomial bound on the number of iterations in this algorithm. This gives a very simple strongly polynomial algorithm that uses no scaling. A variant of the algorithm that uses dynamic trees runs in O(nm(log n) min log (nC), m log n) time on a network of n vertices, m arcs, and arc costs of maximum absolute value C. This bound is comparable to those of the fastest previously known algorithms.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1987
Accession Number
ADA194027

Entities

People

  • Andrew V. Goldberg
  • Robert Tarjan

Organizations

  • Princeton University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Cancellation
  • Computations
  • Computer Science
  • Computers
  • Iterations
  • Linear Programming
  • New Jersey
  • Numbers
  • Polynomials
  • Real Numbers
  • Residuals
  • Sequences
  • Simplex Method
  • Trees (Data Structures)
  • Universities

Fields of Study

  • Computer science
  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Operations Research