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Min-cost multiflows in node-capacitated undirected networks

Author

Listed:
  • Maxim A. Babenko

    (Moscow State University)

  • Alexander V. Karzanov

    (Institute for System Analysis of the RAS)

Abstract

We consider an undirected graph G=(VG,EG) with a set T⊆VG of terminals, and with nonnegative integer capacities c(v) and costs a(v) of nodes v∈VG. A path in G is a T-path if its ends are distinct terminals. By a multiflow we mean a function F assigning to each T-path P a nonnegative rational weight F(P), and a multiflow is called feasible if the sum of weights of T-paths through each node v does not exceed c(v). The value of F is the sum of weights F(P), and the cost of F is the sum of F(P) times the cost of P w.r.t. a, over all T-paths P. Generalizing known results on edge-capacitated multiflows, we show that the problem of finding a minimum cost multiflow among the feasible multiflows of maximum possible value admits half-integer optimal primal and dual solutions. Moreover, we devise a strongly polynomial algorithm for finding such optimal solutions.

Suggested Citation

  • Maxim A. Babenko & Alexander V. Karzanov, 2012. "Min-cost multiflows in node-capacitated undirected networks," Journal of Combinatorial Optimization, Springer, vol. 24(3), pages 202-228, October.
    • Handle: RePEc:spr:jcomop:v:24:y:2012:i:3:d:10.1007_s10878-011-9377-3
    DOI: 10.1007/s10878-011-9377-3
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    References listed on IDEAS

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    1. Andrew V. Goldberg & Alexander V. Karzanov, 1997. "Scaling Methods for Finding a Maximum Free Multiflow of Minimum Cost," Mathematics of Operations Research, INFORMS, vol. 22(1), pages 90-109, February.
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