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#### A Parallelization of Dijkstra's Shortest Path Algorithm

##### MPS-Authors
/persons/resource/persons44266

Crauser,  Andreas
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

/persons/resource/persons45021

Mehlhorn,  Kurt
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

/persons/resource/persons45038

Meyer,  Ulrich
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

/persons/resource/persons45344

Sanders,  Peter
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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##### Citation

Crauser, A., Mehlhorn, K., Meyer, U., & Sanders, P. (1998). A Parallelization of Dijkstra's Shortest Path Algorithm. In L. Brim, J. Gruska, & J. Zlatuška (Eds.), Mathematical Foundations of Computer Science 1998 (pp. 722-731). Berlin, Germany: Springer. doi:10.1007/BFb0055823.

Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-372F-7
##### Abstract
The single source shortest path (SSSP) problem lacks parallel solutions which are fast and simultaneously work-efficient. We propose simple criteria which divide Dijkstra's sequential SSSP algorithm into a number of phases, such that the operations within a phase can be done in parallel. We give a PRAM algorithm based on these criteria and analyze its performance on random digraphs with random edge weights uniformly distributed in $[0,1]$. We use the ${\cal G}(n,d/n)$ model: the graph consists of $n$~nodes and each edge is chosen with probability $d/n$. Our PRAM algorithm needs ${\cal O}(n^{1/3} \log n)$ time and ${\cal O}(n \log n+dn)$ work with high probability (whp). We also give extensions to external memory computation. Simulations show the applicability of our approach even on non-random graphs.