A PTAS for Three-Edge-Connected Survivable Network Design in Planar Graphs
We consider the problem of finding the minimum-weight subgraph that satisfies given connectivity requirements. Specifically, given a requirement r in {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 the input graph is planar and the subgraph may use multiple copies of any given edge (paying for each edge separately). This generalizes an earlier result for r in {0, 1, 2}. In order to achieve this PTAS, we prove some properties of triconnected planar graphs that may be of independent interest.
Three-Edge Connectivity
Polynomial-Time Approximation Schemes
Planar Graphs
3:1-3:13
Regular Paper
Glencora
Borradaile
Glencora Borradaile
Baigong
Zheng
Baigong Zheng
10.4230/LIPIcs.APPROX-RANDOM.2017.3
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