A PTAS for Three-Edge Connectivity in Planar Graphs (1611.03889v1)

Abstract: 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. 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.