By Lars Arge (auth.), Friedhelm Meyer auf der Heide (eds.)
This ebook constitutes the refereed lawsuits of the ninth Annual ecu Symposium on Algorithms, ESA 2001, held in Aarhus, Denmark, in August 2001.
The forty-one revised complete papers offered including 3 invited contributions have been rigorously reviewed and chosen from 102 submissions. The papers are prepared in topical sections on caching and prefetching, on-line algorithms, facts constructions, optimization and approximation, sequences, scheduling, shortest paths, geometry, disbursed algorithms, graph algorithms, pricing, broadcasting and multicasting, graph labeling and graph drawing, and graphs.
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Additional info for Algorithms — ESA 2001: 9th Annual European Symposium Århus, Denmark, August 28–31, 2001 Proceedings
Agarwal and J. Erickson. Geometric range searching and its relatives. In B. Chazelle, J. E. Goodman, and R. Pollack, editors, Advances in Discrete and Computational Geometry, volume 223 of Contemporary Mathematics, pages 1–56. American Mathematical Society, Providence, RI, 1999. 13. A. Aggarwal and J. S. Vitter. The Input/Output complexity of sorting and related problems. Communications of the ACM, 31(9):1116–1127, 1988. 22 L. Arge 14. L. Arge. The buﬀer tree: A new technique for optimal I/O-algorithms.
It is not difficult to prove that when a vertex u becomes settled we have d(u) = δ(s, u), and that d(u) would not change again. An efficient implementation of Dijkstra’s algorithm uses a priority queue to hold the unsettled vertices. The key associated with each unsettled vertex is its tentative distance. Vertices are inserted into the priority queue using insert operations. An unsettled vertex with minimum tentative distance is obtained using an extract-min operation. Tentative distances are updated using decreasekey operations.
1 Nonnegative Real Edge Weights If all the edge weights are nonnegative, we can simply run Dijkstra’s algorithm independently from each vertex. The running time would be O(mn + n2 log n). Karger, Koller and Phillips  and McGeoch  note that by orchestrating the operation of these n Dijkstra’s processes, some unnecessary operations may saved. , the number of edges that actually participate in shortest paths. In the worst case, however, m∗ = m. Karger et al.  also introduce the notion of path-forming algorithms.
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