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.
ASJC Scopus subject areas
- Computer Science(all)