Abstract
In this paper we study a problem named graph partitioning with supply and demand (GPSD), motivated by applications in energy transmission. The input consists of an undirected graph G with the nodes partitioned into two sets: suppliers and consumers. Each supply node has associated a capacity and each consumer node has associated a demand. The goal is to find a subgraph of G and to partition it into trees, such that in each tree: (i) there is precisely one supplier and (ii) the total demand of the consumers is less than or equal to the capacity of the supplier. Moreover, we want to maximize the demand of all the consumers in such a partition.
We also study a variation of the GPSD, termed energy delivery (ED).
In this paper we show the following results:
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1
A 2k-approximation algorithm for the GPSD problem, where k is the number of suppliers. This is the first approximation algorithm proposed for the general case.
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2
A 2-approximation for the GPSD in the case of two suppliers implies a polynomial time algorithm for the famous minimum sum 2-disjoint paths problem, which is not known if it is in P or NP-hard.
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3
The ED problem in the case of two or more suppliers is hard to approximate within any factor, assuming P ≠ NP.
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References
Adams, R.N., Laughton, M.A.: Optimal planning of power networks using mixed-integer programming. part 1: Static and time-phased network synthesis. Proceedings of the Institution of Electrical Engineers 121(2), 139–147 (1974)
Cormen, T.H., Stein, C., Rivest, R.L., Leiserson, C.E.: Introduction to Algorithms, 2nd edn. McGraw-Hill Higher Education (2001)
Crawford, D.M., Holt Jr., S.B.: A mathematical optimization technique for locating and sizing distribution substations, and deriving their optimal service areas. IEEE Transactions on Power Apparatus and Systems 94(2), 230–235 (1975)
El-Kady, M.A.: Computer-aided planning of distribution substation and primary feeders. IEEE Transactions on Power Apparatus and Systems PAS-103(6), 1183–1189 (1984)
Ito, T., Demaine, E.D., Zhou, X., Nishizeki, T.: Approximability of partitioning graphs with supply and demand. Journal of Discrete Algorithms 6(4), 627–650 (2008)
Ito, T., Zhou, X., Nishizeki, T.: Partitioning trees of supply and demand. In: Bose, P., Morin, P. (eds.) ISAAC 2002. LNCS, vol. 2518, pp. 612–623. Springer, Heidelberg (2002)
Ito, T., Zhou, X., Nishizeki, T.: Partitioning graphs of supply and demand. In: ISCAS (1), pp. 160–163 (2005)
Teng, J.H., Lu, C.-N.: Feeder-switch relocation for customer interruption cost minimization. IEEE Transactions on Power Delivery 17(1), 254–259 (2002)
Kersting, W.H., Phillips, W.H., Doyle, R.C.: Distribution feeder reliability studies. In: Rural Electric Power Conference, pp. B4-1–7 (April 1997)
Masud, E.: An interactive procedure for sizing and timing distribution substations using optimization techniques. IEEE Transactions on Power Apparatus and Systems PAS-93(5), 1281–1286 (1974)
Peponis, G.J., Papadopoulos, M.P.: New dynamic, branch exchange method for optimal distribution system planning. IEE Proceedings-Generation, Transmission and Distribution 144(3), 333–339 (1997)
Wall, D.L., Thompson, G.L., Northcote-Green, J.E.D.: An optimization model for planning radial distribution networks. IEEE Transactions on Power Apparatus and Systems PAS-98(3), 1061–1068 (1979)
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Popa, A. (2013). Modelling the Power Supply Network – Hardness and Approximation. In: Chan, TH.H., Lau, L.C., Trevisan, L. (eds) Theory and Applications of Models of Computation. TAMC 2013. Lecture Notes in Computer Science, vol 7876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38236-9_7
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DOI: https://doi.org/10.1007/978-3-642-38236-9_7
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