On Hochbaum's proximity-scaling algorithm for the general resource allocation problem

Satoko Moriguchi, Akiyoshi Shioura

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

It is pointed out that the polynomial-time scaling algorithm by Hochbaum does not work correctly for the general resource allocation problem. Hochbaum's algorithm increases a variable by one unit if the variable cannot feasibly be increased by the scaling unit. We modify the algorithm to increase such a variable by the largest possible amount and show that with this modification the algorithm works correctly. The effect is to modify the factor F in the running time of Hochbaum's algorithm for finding whether a certain solution is feasible by the factor F̃ of finding the maximum feasible increment (also called the saturation capacity). Therefore, the corrected algorithm runs in O(n(log n + F̃) log(B/n)) time.

Original languageEnglish
Pages (from-to)394-397
Number of pages4
JournalMathematics of Operations Research
Volume29
Issue number2
DOIs
Publication statusPublished - 2004 May 1

Keywords

  • Combinatorial optimization
  • Concave function
  • Discrete optimization
  • Resource allocation

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science Applications
  • Management Science and Operations Research

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