Abstract
We study the problem of finding a fractional node-capacitated multiflow of maximum value in an undirected network. Previously known methods for this problem are based on linear programming and the ellipsoid method. In this paper we apply a capacity scaling approach and develop a purely combinatorial weakly polynomial algorithm of time complexity O(Λ(n,m,U) n 2 log2 n logU), where n, m, U are the number of nodes, the number of edges, and the maximum node capacity, respectively, and Λ(n,m,U) denotes the complexity of finding a maximum integer flow in a digraph with n nodes, m edges, and integer arc capacities not exceeding U ∈ ℤ + .
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References
Babenko, M.A.: A fast algorithm for path 2-packing problem. In: Diekert, V., Volkov, M.V., Voronkov, A. (eds.) CSR 2007. LNCS, vol. 4649, pp. 70–81. Springer, Heidelberg (2007)
Cherkassky, B.V.: A solution of a problem on multicommodity flows in a network. Ekonomika i Matematicheskie Metody 13(1), 143–151 (1977)
Ford, L., Fulkerson, D.: Flows in Networds. Princeton University Press, Princeton (1962)
Frank, A.: On connectivity properties of Eulerian digraphs. Ann. Discrete Math. 41, 179–194 (1989)
Goldberg, A.V., Rao, S.: Beyond the flow decomposition barrier. J. ACM 45(5), 783–797 (1998)
Ibaraki, T., Karzanov, A.V., Nagamochi, H.: A fast algorithm for finding a maximum free multiflow in an inner Eulerian network and some generalizations. Combinatorica 18(1), 61–83 (1998)
Karzanov, A.V.: Combinatorial methods to solve cut-dependent multiflow problems. Combinatorial Methods for Flow Problems (Inst. for System Studies, Moscow (3), 6–69 (1979) (in russian)
Karzanov, A.V.: Minimum cost multiflows in undirected networks. Math. Program. 66(3), 313–325 (1994)
Lovász, L.: On some connectivity properties of Eulerian graphs. Acta Math. Akad. Sci. Hung. 28, 129–138 (1976)
Lovász, L.: Matroid matching and some applications. J. Combinatorial Theory, Ser. B 28, 208–236 (1980)
Pap, G.: Some new results on node-capacitated packing of a-paths. In: STOC 2007: Proceedings of the thirty-ninth annual ACM symposium on Theory of computing, pp. 599–604. ACM Press, New York (2007)
Schrijver, A.: Combinatorial Optimization, vol. A, C. Springer, Heidelberg (2003)
Sleator, D., Tarjan, R.: A data structure for dynamic trees. J. Comput. Syst. Sci. 26(3), 362–391 (1983)
Vazirani, V.: Approximation Algorithms. Springer, Heidelberg (2001)
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Babenko, M.A., Karzanov, A.V. (2008). A Scaling Algorithm for the Maximum Node-Capacitated Multiflow Problem. In: Halperin, D., Mehlhorn, K. (eds) Algorithms - ESA 2008. ESA 2008. Lecture Notes in Computer Science, vol 5193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87744-8_11
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DOI: https://doi.org/10.1007/978-3-540-87744-8_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87743-1
Online ISBN: 978-3-540-87744-8
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