## 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 (kn^{2}log n + n^{2}log^{2}n) 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/k^{4} log^{2}k)) if n > k^{4}log^{2}k, and O (k^{5} log^{2}n log cn) if n ≤ k^{4}log^{2}k. If n = Ω (k^{4+qq}) (qq > 0) and c = poly(n), the problem is solved in O (kn) time, which is optimal.

Original language | English |
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Pages (from-to) | 563-578 |

Number of pages | 16 |

Journal | SIAM Journal on Computing |

Volume | 24 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1995 Jan 1 |

Externally published | Yes |

## ASJC Scopus subject areas

- Computer Science(all)
- Mathematics(all)