The Two-Edge Connectivity Survivable-Network Design Problem in Planar Graphs
نویسندگان
چکیده
منابع مشابه
The Two-Edge Connectivity Survivable Network Problem in Planar Graphs
Consider the following problem: given a graph with edgeweights and a subset Q of vertices, find a minimum-weight subgraph in which there are two edge-disjoint paths connecting every pair of vertices in Q. The problem is a failure-resilient analog of the Steiner tree problem, and arises in telecommunications applications. A more general formulation, also employed in telecommunications optimizati...
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We consider the problem of finding the minimum-weight subgraph that satisfies given connectivity requirements. Specifically, given a requirement r ∈ {0, 1, 2, 3} for every vertex, we seek the minimum-weight subgraph that contains, for every pair of vertices u and v, at least min{r(v), r(u)} edge-disjoint u-to-v paths. We give a polynomial-time approximation scheme (PTAS) for this problem when t...
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In the Group Steiner Tree problem (GST), we are given a (vertex or edge)-weighted graph G = (V ,E) on n vertices, together with a root vertex r and a collection of groups {Si}i∈[h] : Si ⊆ V (G). The goal is to find a minimum-cost subgraph H that connects the root to every group. We consider a fault-tolerant variant of GST, which we call Restricted (Rooted) Group SNDP. In this setting, each grou...
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A graph is said to be (k, l)-connected if the resulted graph after removing of any k vertices and (l−1) edges or removing of any (k−1) vertices and l edges is still connected. Beineke and Harary (1967) (see [1]) claimed to prove that there should be k+ l edge-disjoint paths, of which k are vertex-disjoint, between any pair of vertices if the graph has (k, l)-connectivity. However, Mader (1979) ...
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Hershberger, J., M. Rauch and S. Suri, Data structures for two-edge connectivity in planar graphs, Theoretical Computer Science 130 (1994) 139-161. We present a data structure for maintaining 2-edge connectivity information dynamically in an embedded planar graph. The data structure requires linear storage and preprocessing time for its construction, supports online updates (deletion of an edge...
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ژورنال
عنوان ژورنال: ACM Transactions on Algorithms
سال: 2016
ISSN: 1549-6325,1549-6333
DOI: 10.1145/2831235