Abstract
We study a Resilient Shortest Path Problem (RSPP) arising in the literature for the design of communication networks with reliability guarantees. A graph is given, in which every edge has a cost and a probability of availability, and in which two vertices are marked as source and destination. The aim of our RSPP is to find a subgraph of minimum cost, containing a set of paths from the source to the destination vertices, such that the probability that at least one path is available is higher than a given threshold. We explore its theoretical properties and show that, despite a few interesting special cases can be solved in polynomial time, it is in general NP-hard. Computing the probability of availability of a given subgraph is already NP-hard; we therefore introduce an integer relaxation that simplifies the computation of such probability, and we design a corresponding exact algorithm. We present computational results, finding that our algorithm can handle graphs with up to 20 vertices within minutes of computing time.
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Casazza, M., Ceselli, A., Taverna, A. (2018). Mathematical Formulations for the Optimal Design of Resilient Shortest Paths. In: Daniele, P., Scrimali, L. (eds) New Trends in Emerging Complex Real Life Problems. AIRO Springer Series, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-030-00473-6_14
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DOI: https://doi.org/10.1007/978-3-030-00473-6_14
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