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#### Heaps are better than Buckets: Parallel Shortest Paths on Unbalanced Graphs

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##### Citation

Meyer, U. (2001). Heaps are better than Buckets: Parallel Shortest Paths on Unbalanced
Graphs. In R. Sakellariou, J. Keane, J. Gurd, & L. Freeman (*Proceedings
of the 7th International Euro-Par Conference on Parallel Processing (Euro-Par-01):* (pp. 343-351). Berlin, Germany:
Springer.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-3192-4

##### Abstract

We propose a new parallel algorithm for the
single-source shortest-path problem (SSSP). Its
heap data structure is particularly advantageous on graphs with
a moderate number of high degree nodes.
On arbitrary directed graphs with
$n$ nodes, $m$ edges and independent random edge weights
uniformly distributed in the range $[0,1]$ and maximum
shortest path weight $\Diam$ the PRAM version of our algorithm runs in
${\cal O}(\log^2 n \cdot \min_{i} \{2^i \cdot \Diam \cdot \log n+ |V_i| \})$
average-case time using ${\cal O}(n \cdot \log n +m )$ operations
where $|V_i|$ is the number of graph vertices with degree at least $2^i$.
For power-law graph models of the Internet or call graphs
this results in the first work-efficient $o(n^{1/4})$ average-case time
algorithm.