Stochastic Shortest Paths Via Quasi-convex Maximization

  • Evdokia Nikolova
  • Jonathan A. Kelner
  • Matthew Brand
  • Michael Mitzenmacher
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4168)


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(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.


Short Path Extreme Point Edge Length Optimal Path Stochastic Dominance 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Evdokia Nikolova
    • 1
  • Jonathan A. Kelner
    • 1
  • Matthew Brand
    • 1
  • Michael Mitzenmacher
    • 1
  1. 1.MIT CSAIL, MERL, Harvard UniversityCambridge

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