We consider the problem of finding shortest paths in a graph with independent randomly distributed edge lengths. Our goal is to maximize the probability that the path length does not exceed a given threshold value (deadline). We give a surprising exact n⊖(log n) algorithm for the case of normally distributed edge lengths, which is based on quasi-convex maximization. We then prove average and smoothed polynomial bounds for this algorithm, which also translate to average and smoothed bounds for the parametric shortest path problem, and extend to a more general non-convex optimization setting. We also consider a number other edge length distributions, giving a range of exact and approximation schemes. © Springer-Verlag Berlin Heidelberg 2006.
CITATION STYLE
Nikolova, E., Keiner, J. A., Brand, M., & Mitzenmacher, M. (2006). Stochastic shortest paths via quasi-convex maximization. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4168 LNCS, pp. 552–563). Springer Verlag. https://doi.org/10.1007/11841036_50
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