Δ-Stepping : A Parallel Single Source Shortest Path Algorithm

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1461)


In spite of intensive research, little progress has been made towards fast and work-efficient parallel algorithms for the single source shortest path problem. Our Δ-stepping algorithm, a generalization of Dial’s algorithm and the Bellman-Ford algorithm, improves this situation at least in the following “average-case” sense: For random directed graphs with edge probability d/n and uniformly distributed edge weights a PRAM version works in expected time \( \mathcal{O} \)(log3 n/log log n) using linear work. The algorithm also allows for efficient adaptation to distributed memory machines. Implementations show that our approach works on real machines. As a side effect, we get a simple linear time sequential algorithm for a large class of not necessarily random directed graphs with random edge weights.


Short Path Random Graph Short Path Problem Giant Component Heavy Edge 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany

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