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- W2155315809 abstract "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." @default.
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- W2155315809 date "2001-01-01" @default.
- W2155315809 modified "2023-09-27" @default.
- W2155315809 title "A Primal-Dual Approximation Algorithm for the Survivable Network Design Problem in Hypergraph" @default.
- W2155315809 cites W2153014861 @default.
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- W2155315809 doi "https://doi.org/10.1007/3-540-44693-1_42" @default.
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