Efficient Algorithms for the Electric Power Transaction Problem

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(n log n k log(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 + k)2k!) 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.