Abstract
Motivated by multipath routing, we introduce a multi-connected variant of spanners. For that purpose we introduce the p-multipath 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 fault-tolerant spanners, we show how to build p-multipath spanners of constant stretch and of \({\tilde{O}}(n^{1+1/k})\) edges, 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.
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Gavoille, C., Godfroy, Q., Viennot, L. (2011). Node-Disjoint Multipath Spanners and Their Relationship with Fault-Tolerant Spanners. In: Fernàndez Anta, A., Lipari, G., Roy, M. (eds) Principles of Distributed Systems. OPODIS 2011. Lecture Notes in Computer Science, vol 7109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25873-2_11
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DOI: https://doi.org/10.1007/978-3-642-25873-2_11
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