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- W1498454938 abstract "Given a graph H = (U,E) and connectivity requirements r = {r(u,v): u,v ∈ R ⊆ U }, we say that H satisfies r if it contains r(u,v) pairwise internally-disjoint uv-paths for all u,v ∈ R. We consider the Survivable Network with Minimum Number of Steiner Points (SN-MSP) problem: given a finite set V of points in a normed space $(M, left| cdot right|)$ , and connectivity requirements, find a minimum size set S ⊂ M − V of additional points, such that the unit disc graph induced by V ∪ S satisfies the requirements. In the (node-connectivity version of the) Survivable Network Design Problem (SNDP) we are given a graph G = (V,E) with edge costs and connectivity requirements, and seek a min-cost subgraph H of G that satisfies the requirements. Let $k = mathop{ max }limits_{u,v in V}{r(u,v)}$ denote the maximum connectivity requirement. We will show a natural transformation of an SN-MSP instance (V,r) into an SNDP instance (G = (V,E),c,r), such that an α-approximation for the SNDP instance implies an α·O(k 2)-approximation algorithm for the SN-MSP instance. In particular, for the most interesting case of uniform requirement r(u,v) = k for all u,v ∈ V, we obtain for SN-MSP the ratio O(k 2 ln k), which solves an open problem from [3]." @default.
- W1498454938 created "2016-06-24" @default.
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- W1498454938 date "2011-01-01" @default.
- W1498454938 modified "2023-09-23" @default.
- W1498454938 title "Approximating Survivable Networks with Minimum Number of Steiner Points" @default.
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- W1498454938 doi "https://doi.org/10.1007/978-3-642-18318-8_14" @default.
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