Efficient algorithms for the hitchcock transportation problem

Takeshi Tokuyama, Jun Nakano

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Abstract

We consider the Hitchcock transportation problem on n supply points and κ demand points when n is much greater than κ. The problem is solved in O(n2κ log n + n2 log2 n) time if we directly apply an efficient minimum-cost flow algorithm. We show that the complexity can be improved to O(κ2n log2 n) time if n > κ log κ. Further, applying a geometric method named splitter finding and randomization, we improve the time complexity for a case in which the ratio c of the least supply and the maximum supply satisfies the inequality log cn < n/κ4log n. Indeed, if n > κ5 log3 κ and c = poly(n), the problem is solved in O(κn) time, which is optimal.

Original languageEnglish
Title of host publicationProceedings of the 3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992
PublisherAssociation for Computing Machinery
Pages175-184
Number of pages10
ISBN (Electronic)089791466X
Publication statusPublished - 1992 Sep 1
Event3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992 - Orlando, United States
Duration: 1992 Jan 271992 Jan 29

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
VolumePart F129721

Other

Other3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992
CountryUnited States
CityOrlando
Period92/1/2792/1/29

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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