eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-08-11
3:1
3:13
10.4230/LIPIcs.APPROX-RANDOM.2017.3
article
A PTAS for Three-Edge-Connected Survivable Network Design in Planar Graphs
Borradaile, Glencora
Zheng, Baigong
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol081-approx-random2017/LIPIcs.APPROX-RANDOM.2017.3/LIPIcs.APPROX-RANDOM.2017.3.pdf
Three-Edge Connectivity
Polynomial-Time Approximation Schemes
Planar Graphs