Efficient Algorithms for the Electric Power Transaction Problem

  • Masashi Kiyomi
  • Takeaki Uno
  • Tomomi Matsui
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3828)


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 k 5log(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 3)2 k k!) 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.


Electric power transaction minimum cost flow median finding 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Blum, M., Floyd, R.W., Pratt, V., Rivest, R.L., Tarjan, R.E.: Time bounds for selection. Journal of Computer and System Sciences 7, 448–461 (1973)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Edmonds, J., Karp, R.M.: Theoretical improvements in algorithmic efficiency for network flow problems. Journal of the ACM 19, 248–264 (1972)zbMATHCrossRefGoogle Scholar
  3. 3.
    Ford Jr., L.R., Fulkerson, D.R.: Flows in Networks. Princeton University Press, Princeton (1962)zbMATHGoogle Scholar
  4. 4.
    Goldberg, A.V., Tarjan, R.E.: Solving minimum-cost flow problems by successive approximation. In: Proceedings of the 19th Annual ACM Symposium on The Theory of Computing, pp. 7–18 (1987)Google Scholar
  5. 5.
    Goldberg, A.V., Tarjan, R.E.: Finding minimum-cost circulations by canceling negative cycles. Journal of the ACM 36, 873–886 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Klein, M.: A primal method for minimal cost flows with applications to the assignment and transportation problems. Management Science 14, 205–220 (1967)zbMATHCrossRefGoogle Scholar
  7. 7.
    Orlin, J.B.: A faster strongly polynomial minimum cost flow algorithm. In: Proceedings of the 20th Annual ACM Symposium on the Theory of Computing, pp. 377–387 (1988)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Masashi Kiyomi
    • 1
  • Takeaki Uno
    • 1
  • Tomomi Matsui
    • 2
  1. 1.National Institute of InformaticsTokyoJapan
  2. 2.Department of Mathematical Informatics, Graduate School of Information Science and TechnologyUniversity of TokyoTokyoJapan

Personalised recommendations