Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Relaxed heaps: an alternative to Fibonacci heaps with applications to parallel computation
Communications of the ACM
Using selective path-doubling for parallel shortest-path computations
Journal of Algorithms
A randomized parallel algorithm for single-source shortest paths
Journal of Algorithms
A parallel priority queue with constant time operations
Journal of Parallel and Distributed Computing - Parallel and distributed data structures
Time—work tradeoffs of the single-source shortest paths problem
Journal of Algorithms
Trawling the Web for emerging cyber-communities
WWW '99 Proceedings of the eighth international conference on World Wide Web
A random graph model for massive graphs
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Single-source shortest-paths on arbitrary directed graphs in linear average-case time
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
The diameter of random massive graphs
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A Parallelization of Dijkstra's Shortest Path Algorithm
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
Parallel Shortest Path for Arbitrary Graphs
Euro-Par '00 Proceedings from the 6th International Euro-Par Conference on Parallel Processing
Delta-Stepping: A Parallel Single Source Shortest Path Algorithm
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Parallelism in random access machines
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Buckets Strike Back: Improved Parallel Shortest Paths
IPDPS '02 Proceedings of the 16th International Parallel and Distributed Processing Symposium
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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 L the PRAM version of our algorithm runs in O(log2 nċmini{2iċLċlog n+|Vi|}) average-case time using O(nċlog n+m) operations where |Vi| is the number of graph vertices with degree at least 2i. For power-law graph models of the Internet or call graphs this results in the first work-efficient o(n1/4) average-case time algorithm.