Efficient algorithms for the hitchcock transportation problem

Takeshi Tokuyama, Jun Nakano

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

We consider the Hitchcock transportation problem on n supply points and k demand points when n is much greater than k. The problem can be solved in O (kn2log n + n2log2n) time if an efficient minimum-cost flow algorithm is directly applied. Applying a geometric method named splitter finding and a randomization technique, we can improve the time complexity when the ratio c of the maximum supply to the minimum supply is sufficiently small. The expected running time of our randomized algorithm is O (kn log cn/log(n/k4 log2k)) if n > k4log2k, and O (k5 log2n log cn) if n ≤ k4log2k. If n = Ω (k4+qq) (qq > 0) and c = poly(n), the problem is solved in O (kn) time, which is optimal.

Original languageEnglish
Pages (from-to)563-578
Number of pages16
JournalSIAM Journal on Computing
Volume24
Issue number3
DOIs
Publication statusPublished - 1995 Jan 1
Externally publishedYes

ASJC Scopus subject areas

  • Computer Science(all)
  • Mathematics(all)

Fingerprint Dive into the research topics of 'Efficient algorithms for the hitchcock transportation problem'. Together they form a unique fingerprint.

Cite this