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New Bounds for Old Algorithms: On the Average-Case Behavior of Classic Single-Source Shortest-Paths Approaches

  • Ulrich Meyer
  • Andrei Negoescu
  • Volker Weichert
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6595)

Abstract

Despite disillusioning worst-case behavior, classic algorithms for single-source shortest-paths (SSSP) like Bellman-Ford are still being used in practice, especially due to their simple data structures. However, surprisingly little is known about the average-case complexity of these approaches. We provide new theoretical and experimental results for the performance of classic label-correcting SSSP algorithms on graph classes with non-negative random edge weights. In particular, we prove a tight lower bound of Ω(n 2) for the running times of Bellman-Ford on a class of sparse graphs with O(n) nodes and edges; the best previous bound was Ω(n 4/3 − ε ). The same improvements are shown for Pallottino’s algorithm. We also lift a lower bound for the approximate bucket implementation of Dijkstra’s algorithm from Ω(n logn / loglogn) to Ω(n 1.2 − ε ). Furthermore, we provide an experimental evaluation of our new graph classes in comparison with previously used test inputs.

Keywords

Graph Class Short Path Algorithm Grid Graph FIFO Queue Bucket Size 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Ulrich Meyer
    • 1
  • Andrei Negoescu
    • 1
  • Volker Weichert
    • 1
  1. 1.Institut für InformatikGoethe-Universität Frankfurt am MainGermany

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