TY - GEN

T1 - Efficient algorithms for the hitchcock transportation problem

AU - Tokuyama, Takeshi

AU - Nakano, Jun

PY - 1992/9/1

Y1 - 1992/9/1

N2 - 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.

AB - 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.

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M3 - Conference contribution

AN - SCOPUS:19544374053

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 175

EP - 184

BT - Proceedings of the 3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992

PB - Association for Computing Machinery

T2 - 3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992

Y2 - 27 January 1992 through 29 January 1992

ER -