Computing edge-connectivity in multigraphs and capacitated graphs
SIAM Journal on Discrete Mathematics
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Journal of the ACM (JACM)
Beyond the flow decomposition barrier
Journal of the ACM (JACM)
A note on minimizing submodular functions
Information Processing Letters
Flows in Undirected Unit Capacity Networks
SIAM Journal on Discrete Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Source location in undirected and directed hypergraphs
Operations Research Letters
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This paper deals with the problem of finding a minimum-cost vertex subset S in an undirected network such that for each vertex v we can send d(v) units of flow from S to v. Although this problem is NP-hard in general, Tamura et al. have presented a greedy algorithm for solving the special case with uniform costs on the vertices. We give a simpler proof on the validity of the greedy algorithm using linear programming duality and improve the running time bound from O(n2M) to O(nM), where n is the number of vertices in the network and M denotes the time for max-flow computation in the network with n vertices and m edges. We also present an O(n(m+n log n)) time algorithm for the special case with uniform demands and arbitrary costs.