Graph augmentation and related problems: theory and practice
Graph augmentation and related problems: theory and practice
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Generalized submodular cover problems and applications
Theoretical Computer Science
Minimum cost source location problem with vertex-connectivity requirements in digraphs
Information Processing Letters
Locating sources to meet flow demands in undirected networks
Journal of Algorithms
Minimum cost source location problems with flow requirements
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Journal of Discrete Algorithms
Approximating minimum cost source location problems with local vertex-connectivity demands
Journal of Discrete Algorithms
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We consider Source Location (SL) problems: given a capacitated network G=(V,E), cost c(v) and a demand d(v) for every v@?V, choose a min-cost S@?V so that @l(v,S)=d(v) holds for every v@?V, where @l(v,S) is the maximum flow value from v to S. In the directed variant, we have demands d^i^n(v) and d^o^u^t(v) and we require @l(S,v)=d^i^n(v) and @l(v,S)=d^o^u^t(v). Undirected SL is (weakly) NP-hard on stars with r(v)=0 for all v except the center. But, it is known to be polynomially solvable for uniform costs and uniform demands. For general instances, both directed an undirected SL admit a (lnD+1)-approximation algorithms, where D is the sum of the demands; up to constant this is tight, unless P=NP. We give a pseudopolynomial algorithm for undirected SL on trees with running time O(|V|@D^3), where @D=max"v"@?"Vd(v). This algorithm is used to derive a linear time algorithm for undirected SL with @D=