By Lars Arge (auth.), Friedhelm Meyer auf der Heide (eds.)
This publication constitutes the refereed court cases of the ninth Annual eu Symposium on Algorithms, ESA 2001, held in Aarhus, Denmark, in August 2001.
The forty-one revised complete papers provided 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 resources for Algorithms — ESA 2001: 9th Annual European Symposium Århus, Denmark, August 28–31, 2001 Proceedings
G. C. Resende, editors, Handbook of Massive Data Sets. Kluwer Academic Publishers, 2001. (To appear). 17. L. Arge, R. Barve, O. Procopiuc, L. Toma, D. E. Vengroﬀ, and R. Wickremesinghe. 01a). Duke University, 1999. edu/TPIE/. 18. L. Arge, G. S. Brodal, and L. Toma. On external memory MST, SSSP and multiway planar graph separation. In Proc. Scandinavian Workshop on Algorithms Theory, LNCS 1851, pages 433–447, 2000. 19. L. Arge, J. Chase, P. Halpin, L. Toma, D. Urban, J. Vitter, and R. Wickremesinghe.
If there is no (directed) path from u to v in the graph, we define δ(u, v) = +∞. If all the edge weights are nonnegative, then all distances are well defined. If the graph contains (directed) cycles of negative weight, and there is a path from u to v that passes through such a negative cycle, we let δ(u, v) = −∞. Shortest paths from a source vertex s to all other vertices of the graph can be compactly represented using a tree of shortest paths. This is a tree, rooted at s, that spans all the vertices reachable from s in the graph, such that for every vertex v reachable from s in the graph, the unique path in the tree from s to v is a shortest path from s to v in the graph.
In a sharp contract, Thorup [68,69] developed recently an elegant algorithm that avoids the rigid settling order of Dijkstra’s algorithm. Thorup’s algorithm bypasses the sorting bottleneck and runs in optimal O(m) time! His algorithm works, however, only on undirected graphs. It remains an open problem whether extensions of his ideas could could be used to obtain a similar result for directed graphs. 4 U. Zwick Positive and Negative Real Edge Weights We now allow, for the first time, negative edge weights.
Algorithms — ESA 2001: 9th Annual European Symposium Århus, Denmark, August 28–31, 2001 Proceedings by Lars Arge (auth.), Friedhelm Meyer auf der Heide (eds.)