Fault-tolerant spanners for general graphs

The paper concerns graph spanners that are resistant to vertex or edge failures. Given a weighted undirected n-vertex graph G = (V, E) and an integer k 1, the subgraph H = (V, E ), E E, is a spanner of stretch k (or, a kspanner) of G if H (u, v) k ? G(u, v) for every u, v V , where G (u, v) denotes the distance between u and v in G . Graph spanners were extensively studied since their introduction over two decades ago. It is known how to efficiently construct a (2k-1)-spanner of size O(n1+1/k ), and this sizestretch tradeoff is conjectured to be tight. The notion of fault tolerant spanners was introduced a decade ago in the geometric setting [Levcopoulos et al., STOC'98]. A subgraph H is an f-vertex fault tolerant kspanner of the graph G if for any set F V of size at most f and any pair of vertices u, v V \ F, the distances in H satisfy H\F (u, v) k ? G\F (u, v). Levcopoulos et al. presented an efficient algorithm that given a set S of n points in Rd , constructs an f-vert...

• Type: Conference
• Year: 2009
• Where: STOC
• Authors: Shiri Chechik, Michael Langberg, David Peleg, Liam Roditty
• Keywords: Algorithms, F-vertex Fault Tolerant, Fault Tolerant, Fault Tolerant Spanners, STOC 2009