Abstract
We show how to compute single-source shortest paths in undirected graphs with non-negative edge lengths in \({\mathcal{O}}(\sqrt{nm/B}\log n + {\mathit{MST}}(n,m))\) I/Os, where n is the number of vertices, m is the number of edges, B is the disk block size, and MST(n,m) is the I/O-cost of computing a minimum spanning tree. For sparse graphs, the new algorithm performs \({\mathcal{O}}((n/\sqrt{B})\log n)\) I/Os. This result removes our previous algorithm’s dependence on the edge lengths in the graph.
For more details, see [10].
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References
Aggarwal, A., Vitter, J.S.: The input/output complexity of sorting and related problems. Comm. ACM, 1116–1127 (1988)
Arge, L., Brodal, G.S., Toma, L.: On external-memory MST, SSSP and multi-way planar graph separation. J. Alg. 53(2), 186–206 (2004)
Arge, L., Toma, L., Zeh, N.: I/O-efficient algorithms for planar digraphs. In: Proc. 15th SPAA, pp. 85–93 (2003)
Buchsbaum, A.L., Goldwasser, M., Venkatasubramanian, S., Westbrook, J.R.: On external memory graph traversal. In: Proc. 11th SODA, pp. 859–860 (2000)
Chiang, Y.-J., Goodrich, M.T., Grove, E.F., Tamassia, R., Vengroff, D.E., Vitter, J.S.: External-memory graph algorithms. In: Proc. 6th SODA, pp. 139–149 (1995)
Dijkstra, E.W.: A note on two problems in connection with graphs. Num. Math. 1, 269–271 (1959)
Kumar, V., Schwabe, E.J.: Improved algorithms and data structures for solving graph problems in external memory. In: Proc. 8th SPDP, pp. 169–176 (1996)
Mehlhorn, K., Meyer, U.: External-memory breadth-first search with sublinear I/O. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 723–735. Springer, Heidelberg (2002)
Meyer, U., Zeh, N.: I/O-efficient undirected shortest paths. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 434–445. Springer, Heidelberg (2003)
Meyer, U., Zeh, N.: I/O-efficient undirected shortest paths with unbounded weights. Tech. Report CS-2006-04, Faculty of Comp. Sci., Dalhousie Univ. (2006)
Pettie, S., Ramachandran, V.: Computing shortest paths with comparisons and additions. In: Proc. 13th SODA, pp. 267–276 (2002)
Thorup, M.: Undirected single source shortest paths with positive integer weights in linear time. J. ACM 46, 362–394 (1999)
Thorup, M.: Floats, integers, and single source shortest paths. J. Alg. 35, 189–201 (2000)
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Meyer, U., Zeh, N. (2006). I/O-Efficient Undirected Shortest Paths with Unbounded Edge Lengths. In: Azar, Y., Erlebach, T. (eds) Algorithms – ESA 2006. ESA 2006. Lecture Notes in Computer Science, vol 4168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11841036_49
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DOI: https://doi.org/10.1007/11841036_49
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