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Shortest Paths with Shortest Detours
Journal of Optimization Theory and Applications, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Carolin Torchiani +3 more
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Shortest paths in euclidean graphs
Algorithmica, 1986We analyze a simple method for finding shortest paths in Euclidean graphs (where vertices are points in a Euclidean space and edge weights are Euclidean distances between points). For many graph models, the average running time of the algorithm to find the shortest path between a specified pair of vertices in a graph with V vertices and E edges is ...
Sedgewick, Robert, Vitter, Jeffrey Scott
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All pairs almost shortest paths
Proceedings of 37th Conference on Foundations of Computer Science, 2000Summary: Let \(G=(V,E)\) be an unweighted undirected graph on \(n\) vertices. A simple argument shows that computing all distances in \(G\) with an additive one-sided error of at most 1 is as hard as Boolean matrix multiplication. Building on recent work of \textit{D. Aingworth, C. Chekuri, P. Indyk} and \textit{R. Motwani} [SIAM J. Comput. 28, No.
Dor, Dorit, Halperin, Shay, Zwick, Uri
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Shortest Path Geometric Rounding
Algorithmica, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The shortest path tree problem is a classical and widely studied combinatorial problem. The scope of this article is to provide an extensive treatment of the major classical approaches. It then proceeds focusing on the auction algorithm and some of its recently developed variants.
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1986
Recently there has been considerable research activity on algorithms for finding shortest paths in geometries induced by obstacles. A typical problem is finding the shortest path between two points on the Euclidean plane avoiding a given set of polygonal obstacles (see Figure 1). We review this area and isolate several interesting open problems.
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Recently there has been considerable research activity on algorithms for finding shortest paths in geometries induced by obstacles. A typical problem is finding the shortest path between two points on the Euclidean plane avoiding a given set of polygonal obstacles (see Figure 1). We review this area and isolate several interesting open problems.
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