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NodeDisjoint Multipath Spanners and their Relationship with FaultTolerant Spanners
, 2011
"... Motivated by multipath routing, we introduce a multiconnected variant of spanners. For that purpose we introduce the pmultipath cost between two nodes u and v as the minimum weight of a collection of p internally vertexdisjoint paths between u and v. Given a weighted graph G, a subgraph H is a p ..."
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Motivated by multipath routing, we introduce a multiconnected variant of spanners. For that purpose we introduce the pmultipath cost between two nodes u and v as the minimum weight of a collection of p internally vertexdisjoint paths between u and v. Given a weighted graph G, a subgraph H is a pmultipath sspanner if for all u, v, the pmultipath cost between u and v in H is at most s times the pmultipath cost in G. The s factor is called the stretch. Building upon recent results on faulttolerant spanners, we show how to build pmultipath spanners of constant stretch and of Õ(n1+1/k) edges 1, for fixed parameters p and k, n being the number of nodes of the graph. Such spanners can be constructed by a distributed algorithm running in O(k) rounds. Additionally, we give an improved construction for the case p = k = 2. Our spanner H has O(n 3/2) edges and the pmultipath cost in H between any two node is at most twice the corresponding one in G plus O(W), W being the maximum edge weight.
Multipath spanners via faulttolerant spanners
 In The 1st Mediterranean Conference on Algorithms (MEDALG
, 2012
"... Abstract. An sspanner 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 pmultipath distance, defined as the smallest ..."
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Abstract. An sspanner 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 pmultipath distance, defined as the smallest length of a collection of p pairwise (vertex or edge) disjoint paths. The notion of multipath spanners was introduced in [15, 16] for edge (respectively, vertex) disjoint paths. This paper significantly improves the stretchsize tradeoff result of the two previous papers, using the related concept of faulttolerant sspanners, introduced in [6] for general 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 smultipath spanner, thereby improving on the large stretch obtained in [15, 16]. 1