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 \( \mathcal{L} \) the PRAM version of our algorithm runs in \( \mathcal{O}\left( {log^2 n \cdot \min _i \left\{ {2^i \cdot \mathcal{L} \cdot log n + \left| {V_i } \right|} \right\}} \right) \) average-case time using \( \mathcal{O}\left( {n \cdot log n + m} \right) \) operations where |V i| 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(n 1/4) average-case time algorithm.
Partially supported by the IST Programme of the EU under contract number IST-1999-14186 (ALCOM-FT).
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References
W. Aiello, F. Chung, and L. Lu. A random graph model for massive graphs. In Proc. 32nd Annual ACM Symposium on Theory of Computing, pages 171–180.ACM, 2000.
K. B. Athreya and P. Ney. Branching Processes. Springer, 1972.
A. Barabasi and R. Albert. Emergence of scaling in random networks. Science, 286:509–512, 1999.
B. Bollobás. Random Graphs. Academic Press, 1985.
G. S. Brodal, J. L. Träff, and C. D. Zaroliagis. A parallel priority queue with constant time operations. Journal of Parallel and Distributed Computing, 49(1):4–21, 1998.
E. Cohen. Using selective path-doubling for parallel shortest-path computations. Journal of Algorithms, 22(1):30–56, January 1997.
A. Crauser, K. Mehlhorn, U. Meyer, and P. Sanders. A parallelization of Dijkstra’s shortest path algorithm. In 23rd Symp. on Mathematical Foundations of Computer Science, volume 1450 of LNCS, pages 722–731. Springer, 1998.
E. W. Dijkstra. A note on two problems in connexion with graphs. Num. Math., 1:269–271, 1959.
J. R. Driscoll, H. N. Gabow, R. Shrairman, and R. E. Tarjan. Relaxed heaps: An alternative to fibonacci heaps with applications to parallel computation. Communications of the ACM, 31, 1988.
S. Fortune and J. Wyllie. Parallelism in random access memories. In Proc. 10th Symp. on the Theory of Computing, pages 114–118. ACM, 1978.
M. L. Fredman and R. E. Tarjan. Fibonacci heaps and their uses in improved network optimization algorithms. Journal of the ACM, 34:596–615, 1987.
Y. Han, V. Pan, and J. Reif. Efficient parallel algorithms for computing all pair shortest paths in directed graphs. Algorithmica, 17(4):399–415, 1997.
T. Harris. The Theory of Branching Processes. Springer, 1963.
P. Klein and S. Subramanian. A randomized parallel algorithm for single-source shortest paths. Journal of Algorithms, 25(2):205–220, November 1997.
R. Kumar, P. Raghavan, S. Rajagopalan, and A. Tomkins. Trawling the web for emerging cyber-communities. In Proc. 8th International World-Wide Web Conference, 1999.
L. Lu. The diameter of random massive graphs. In Proc. 12th Annual Symposium on Discrete Algorithms, pages 912–921., 2001.
U. Meyer. Single-source shortest-paths on arbitrary directed graphs in linear average-case time. In Proc. 12th Annual Symposium on Discrete Algorithms, pages 797–806. ACM-SIAM, 2001.
U. Meyer and P. Sanders. ∇-stepping: A parallel shortest path algorithm. In 6th European Symposium on Algorithms (ESA), volume 1461 of LNCS, pages 393–404. Springer, 1998.
U. Meyer and P. Sanders. Parallel shortest path for arbitrary graphs. In Proc. Euro-Par 2000 Parallel Processing, volume 1900 of LNCS, pages 461–470. Springer, 2000.
H. Shi and T. H. Spencer. Time-work tradeoffs of the single-source shortest paths problem. Journal of Algorithms, 30(1):19–32, 1999.
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Meyer, U. (2001). Heaps Are Better than Buckets: Parallel Shortest Paths on Unbalanced Graphs. In: Sakellariou, R., Gurd, J., Freeman, L., Keane, J. (eds) Euro-Par 2001 Parallel Processing. Euro-Par 2001. Lecture Notes in Computer Science, vol 2150. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44681-8_49
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