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6,963
Finding the k Shortest Paths
, 1997
"... We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m + n log n + k). We can also find the k shortest pat ..."
Abstract
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Cited by 401 (2 self)
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We give algorithms for finding the k shortest paths (not required to be simple) connecting a pair of vertices in a digraph. Our algorithms output an implicit representation of these paths in a digraph with n vertices and m edges, in time O(m + n log n + k). We can also find the k shortest
On shortest path representation
"... Abstract—Lately, it has been proposed to use shortest path first ..."
Abstract
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Cited by 5 (2 self)
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Abstract—Lately, it has been proposed to use shortest path first
On dynamic shortest paths problems
, 2004
"... We obtain the following results related to dynamic versions of the shortest-paths problem: (i) Reductions that show that the incremental and decremental single-source shortest-paths problems, for weighted directed or undirected graphs, are, in a strong sense, at least as hard as the static all-pairs ..."
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Cited by 41 (2 self)
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We obtain the following results related to dynamic versions of the shortest-paths problem: (i) Reductions that show that the incremental and decremental single-source shortest-paths problems, for weighted directed or undirected graphs, are, in a strong sense, at least as hard as the static all
The Geodesic Shortest Path
"... Abstract. In the geodesic shortest path problem we have to find the shortest path between two points on the boundary of a polyhedron. The shortest path must lead along the surface of the polyhedron. In the article, the description and solution of that problem is given. The case with forbidden areas ..."
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Abstract. In the geodesic shortest path problem we have to find the shortest path between two points on the boundary of a polyhedron. The shortest path must lead along the surface of the polyhedron. In the article, the description and solution of that problem is given. The case with forbidden areas
Geometric Shortest Paths and Network Optimization
- Handbook of Computational Geometry
, 1998
"... Introduction A natural and well-studied problem in algorithmic graph theory and network optimization is that of computing a "shortest path" between two nodes, s and t, in a graph whose edges have "weights" associated with them, and we consider the "length" of a path to ..."
Abstract
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Cited by 187 (15 self)
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Introduction A natural and well-studied problem in algorithmic graph theory and network optimization is that of computing a "shortest path" between two nodes, s and t, in a graph whose edges have "weights" associated with them, and we consider the "length" of a path
Shortest-Path Kernels on Graphs
- In Proceedings of the 2005 International Conference on Data Mining
, 2005
"... Data mining algorithms are facing the challenge to deal with an increasing number of complex objects. For graph data, a whole toolbox of data mining algorithms becomes available by defining a kernel function on instances of graphs. Graph kernels based on walks, subtrees and cycles in graphs have bee ..."
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Cited by 62 (5 self)
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propose graph kernels based on shortest paths. These kernels are computable in polynomial time, retain expressivity and are still positive definite. In experiments on classification of graph models of proteins, our shortest-path kernels show significantly higher classification accuracy than walk
Shortest path algorithms techniques
, 2013
"... Shortest paths, or close to shortest paths, are commonly used in everyday situations. The paper reviews the various algorithms available for the problem. One of the famous technique Dijkstra’s algorithm solves the single-source shortest path problem on any directed graph in O(m+nlogn) worst-case tim ..."
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Shortest paths, or close to shortest paths, are commonly used in everyday situations. The paper reviews the various algorithms available for the problem. One of the famous technique Dijkstra’s algorithm solves the single-source shortest path problem on any directed graph in O(m+nlogn) worst
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