Abstract
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) disjoint paths. The notion of multipath spanners was introduced in [15,16] for edge (respectively, vertex) disjoint paths. This paper significantly improves the stretch-size tradeoff result of the two previous papers, using the related concept of fault-tolerant s-spanners, 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 s-multipath spanner, thereby improving on the large stretch obtained in [15,16].
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Chechik, S., Godfroy, Q., Peleg, D. (2012). Multipath Spanners via Fault-Tolerant Spanners. In: Even, G., Rawitz, D. (eds) Design and Analysis of Algorithms. MedAlg 2012. Lecture Notes in Computer Science, vol 7659. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34862-4_8
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DOI: https://doi.org/10.1007/978-3-642-34862-4_8
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