Solving minimum-cost flow problems by successive approximation
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
A faster strongly polynomial minimum cost flow algorithm
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Finding minimum-cost circulations by canceling negative cycles
Journal of the ACM (JACM)
Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Journal of the ACM (JACM)
Journal of Computer and System Sciences
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We present two efficient algorithms for solving the electric power transaction problem. The electric power transaction problem appears when maximizing the social benefit on electric power transactions among some private companies. The problem is a special case of the minimum cost flow problem defined on a network with many leaves, where each leaf corresponds to a (private) company who wants to sell or buy electric power. Our first algorithm is based on the minimum mean cycle canceling algorithm and the second algorithm uses a linear time median finding algorithm. The first algorithm finds an optimal solution in O(nlogn k5log(kC)) time where n is the number of leaves, k is the number of non-leaf vertices and C is the highest electric power price per unit that companies may offer. The time complexity of the second algorithm is bounded by O((n+k3)2kk!) time, which is linear in n. In many practical instances, k is small and n is very large, hence these algorithms solve the problem more efficiently than the ordinary network flow algorithms.