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#### A Parallel Priority Queue with Constant Time Operations

##### MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44187

Brodal,  Gerth Stølting
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45632

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

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45787

Zaroliagis,  Christos
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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##### Zitation

Brodal, G. S., Träff, J. L., & Zaroliagis, C. (1998). A Parallel Priority Queue with Constant Time Operations. Journal of Parallel and Distributed Computing, Special Issue on Parallel Data Structures, 49(1), 4-21.

We present a parallel priority queue that supports the following operations in constant time: {\em parallel insertion\/} of a sequence of elements ordered according to key, {\em parallel decrease key\/} for a sequence of elements ordered according to key, {\em deletion of the minimum key element}, as well as {\em deletion of an arbitrary element}. Our data structure is the first to support multi insertion and multi decrease key in constant time. The priority queue can be implemented on the EREW PRAM, and can perform any sequence of $n$ operations in $O(n)$ time and $O(m\log n)$ work, $m$ being the total number of keys inserted and/or updated. A main application is a parallel implementation of Dijkstra's algorithm for the single-source shortest path problem, which runs in $O(n)$ time and $O(m\log n)$ work on a CREW PRAM on graphs with $n$ vertices and $m$ edges. This is a logarithmic factor improvement in the running time compared with previous approaches.