A new approach to the maximum-flow problem
Journal of the ACM (JACM)
A general approximation technique for constrained forest problems
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
A primal-dual approximation algorithm for generalized Steiner network problems
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
The primal-dual method for approximation algorithms and its application to network design problems
Approximation algorithms for NP-hard problems
Improved approximation algorithms for network design problems
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
A primal-dual schema based approximation algorithm for the element connectivity problem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A Factor 2 Approximation Algorithm for the Generalized Steiner Network Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
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Given a hypergraph with nonnegative costs on hyperedge and a requirement function r : 2V → Z+, where V is the vertex set, we consider the problem of finding a minimum cost hyperedge set F such that for all S ⊆ V, F contains at least r(S) hyperedges incident to S. In the case that r is weakly supermodular (i.e., r(V) = 0 and r(A) + r(B) ≤ max{r(A ∩ B) + r(A ∪ B); r(A - B) + r(B - A)} for any A;B ⊆ V), and the so-called minimum violated sets can be computed in polynomial time, we present a primal-dual approximation algorithm with performance guarantee dmaxH(rmax), where dmax is the maximum degree of the hyperedges with positive cost, rmax is the maximum requirement, and H(i) = Σi=1i 1/j is the harmonic function. In particular, our algorithm can be applied to the survivable network design problem in which the requirement is that there should be at least rst hyperedge-disjoint paths between each pair of distinct vertices s and t, for which rst is prescribed.