Minimum cost multiflows in undirected networks
Mathematical Programming: Series A and B
Scaling methods for finding a maximum free multiflow of minimum cost
Mathematics of Operations Research
Approximation algorithms
Maximum skew-symmetric flows and matchings
Mathematical Programming: Series A and B
Some new results on node-capacitated packing of A-paths
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Free multiflows in bidirected and skew-symmetric graphs
Discrete Applied Mathematics
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We consider an undirected graph G=(VG,EG) with a set T驴VG of terminals, and with nonnegative integer capacities c(v) and costs a(v) of nodes v驴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.