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Stochastic Shortest Paths Via Quasi-convex Maximization

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Algorithms – ESA 2006 (ESA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4168))

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Abstract

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 Θ(logn) 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.

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Author information

Authors and Affiliations

  1. MIT CSAIL, MERL, Harvard University, Cambridge, MA

    Evdokia Nikolova, Jonathan A. Kelner, Matthew Brand & Michael Mitzenmacher

Authors
  1. Evdokia Nikolova
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  2. Jonathan A. Kelner
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  3. Matthew Brand
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  4. Michael Mitzenmacher
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Editor information

Editors and Affiliations

  1. Microsoft Research, One Microsoft Way, Redmond, WA 98052, USA and School of Computer Science, Tel-Aviv University, 69978, Tel-Aviv, Israel

    Yossi Azar

  2. Department of Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Thomas Erlebach

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© 2006 Springer-Verlag Berlin Heidelberg

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Nikolova, E., Kelner, J.A., Brand, M., Mitzenmacher, M. (2006). Stochastic Shortest Paths Via Quasi-convex Maximization. In: Azar, Y., Erlebach, T. (eds) Algorithms – ESA 2006. ESA 2006. Lecture Notes in Computer Science, vol 4168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11841036_50

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  • DOI: https://doi.org/10.1007/11841036_50

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-38875-3

  • Online ISBN: 978-3-540-38876-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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