Node-Disjoint Multipath Spanners and Their Relationship with Fault-Tolerant Spanners [chapter]

Cyril Gavoille, Quentin Godfroy, Laurent Viennot
2011 Lecture Notes in Computer Science  
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 vertex-disjoint paths between u and v. Given a weighted graph G, a subgraph H is a p-multipath s-spanner if for all u, v, the p-multipath cost between u and v in H is at most s times the p-multipath cost in G. The s factor is called the stretch. Building upon recent results on
more » ... erant spanners, we show how to build p-multipath spanners of constant stretch and ofÕ(n 1+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 p-multipath 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.
doi:10.1007/978-3-642-25873-2_11 fatcat:gkkrferctzcxpec4ffymmrnty4