Multipath Spanners

Abstract. This paper concerns graph spanners that approximate multipaths between pair of vertices of an undirected graphs with n vertices. Classically, a spanner H of stretch s for a graph G is a spanning subgraph such that the distance in H between any two vertices is at most s times the distance in G. We study in this paper spanners that approximate short cycles, and more generally p edge-disjoint paths with p > 1, between any pair of vertices. For every unweighted graph G, we construct a 2-multipath 3-spanner of O(n3/2 ) edges. In other words, for any two vertices u, v of G, the length of the shortest cycle (with no edge replication) traversing u, v in the spanner is at most thrice the length of the shortest one in G. This construction is shown to be optimal in term of stretch and of size. In a second construction, we produce a 2-multipath (2, 8)-spanner of O(n3/2 ) edges, i.e., the length of the shortest cycle traversing any two vertices have length at most twice the shortest le...

• Type: Conference
• Year: 2010
• Where: SIROCCO
• Authors: Cyril Gavoille, Quentin Godfroy, Laurent Viennot
• Keywords: Information Technology, Paper Concerns Graph, Shortest Cycle, SIROCCO 2010, Unweighted Graph G