Multipath Spanners via Fault-Tolerant Spanners

Shiri Chechik (1) , Quentin Godfroy (2) , David Peleg (1)

1 Department of Computer Science and Applied Mathematics [Rehovot]
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

An s-spanner H of a graph G is a subgraph such that the distance between any two vertices u and v in H is greater by at most a multiplicative factor s than the distance in G. In this paper, we focus on an extension of the concept of spanners to p-multipath distance, defined as the smallest length of a collection of p pairwise (vertex or edge) dis- joint paths. The notion of multipath spanners was introduced in [15, 16] for edge (respectively, vertex) disjoint paths. This paper significantly im- proves the stretch-size tradeoff result of the two previous papers, using the related concept of fault-tolerant s-spanners, introduced in [6] for gen- eral graphs. More precisely, we show that at the cost of increasing the number of edges by a polynomial factor in p and s, it is possible to obtain an s-multipath spanner, thereby improving on the large stretch obtained in [15, 16].

Mots clés: graphs; spanners

Domaines: Algorithme et structure de données [cs.DS]

Shiri Chechik, Quentin Godfroy, David Peleg. Multipath Spanners via Fault-Tolerant Spanners. 1st Mediterranean Conference on Algorithms (MEDALG), Dec 2012, Kibbutz Ein Gedi, Israel. pp.108-119, ⟨10.1007/978-3-642-34862-4_8⟩. ⟨hal-00984946⟩