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If cycles are allowed, the previous algorithm does not work. This is because, there may not be any node with zero outgoing edges. So, potentially there is no node which can terminate without consulting other nodes. The Dijkstra–Scholten algorithm solves this problem by implicitly creating a spanning tree of the graph. A spanning-tree is a ...
The contraction hierarchies (CH) algorithm is a two-phase approach to the shortest path problem consisting of a preprocessing phase and a query phase.As road networks change rather infrequently, more time (seconds to hours) can be used to once precompute some calculations before queries are to be answered.
The goal of the all-pair-shortest-paths problem is to find the shortest path between all pairs of nodes of the graph. For this path to be unique it is required that the graph does not contain cycles with a negative weight. In the remainder of the article it is assumed that the graph is represented using an adjacency matrix.
The Euclidean shortest path problem is a problem in computational geometry: given a set of polyhedral obstacles in a Euclidean space, and two points, find the shortest path between the points that does not intersect any of the obstacles.
The k shortest path routing problem is a generalization of the shortest path routing problem in a given network. It asks not only about a shortest path but also about next k−1 shortest paths (which may be longer than the shortest path). A variation of the problem is the loopless k shortest paths.
Therefore, the shortest two disjoint paths under the modified weights are the same paths as the shortest two paths in the original graph, although they have different weights. Suurballe's algorithm may be seen as a special case of the successive shortest paths method for finding a minimum cost flow with total flow amount two from s to t. The ...
Average path length, or average shortest path length is a concept in network topology that is defined as the average number of steps along the shortest paths for all possible pairs of network nodes. It is a measure of the efficiency of information or mass transport on a network.
Edge disjoint shortest pair algorithm is an algorithm in computer network routing. [1] The algorithm is used for generating the shortest pair of edge disjoint paths between a given pair of vertices. For an undirected graph G(V, E), it is stated as follows: Run the shortest path algorithm for the given pair of vertices