Efficient algorithms for the Hitchcock transportation problem

Authors:
Takeshi Tokuyama;Jun Nakano
Affiliations:
-;-
Venue:
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Year:
1992

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Abstract

We consider the Hitchcock transportation problem on n supply points and k demand points when n is much greater than k. The problem is solved in O(n2k log n + n2 log2 n) time if n k log k. 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/k4 log n. Indeed, if n k5 log3 k and c = poly(n), the problem is solved in O(kn) time, which is optimal.