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Dijkstra's algorithm (/ ˈdaɪkstrəz / DYKE-strəz) is an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, road networks. It was conceived by computer scientist Edsger W. Dijkstra in 1956 and published three years later. [4][5][6] Dijkstra's algorithm finds the shortest path from a ...
Shortest path problem. Shortest path (A, C, E, D, F) between vertices A and F in the weighted directed graph. In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. [1]
The Hamiltonian path problem is a topic discussed in the fields of complexity theory and graph theory. It decides if a directed or undirected graph, G, contains a Hamiltonian path, a path that visits every vertex in the graph exactly once. The problem may specify the start and end of the path, in which case the starting vertex s and ending ...
k shortest path routing. k. shortest path routing. 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.
Path (graph theory) In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct (and since the vertices are distinct, so are the edges). A directed path (sometimes called dipath[1]) in a directed graph is a finite or infinite sequence of edges which ...
This symmetry halves the number of possible solutions. In the asymmetric TSP, paths may not exist in both directions or the distances might be different, forming a directed graph. Traffic congestion, one-way streets, and airfares for cities with different departure and arrival fees are real-world considerations that could yield a TSP problem in ...
Two vertices in a directed graph are said to be strongly connected to each other if there is a directed path from one to the other and vice versa. This is an equivalence relation , and the vertices of the graph may be partitioned into strongly connected components, subsets within which every two vertices are strongly connected.
In graph algorithms, the widest path problem is the problem of finding a path between two designated vertices in a weighted graph, maximizing the weight of the minimum-weight edge in the path. The widest path problem is also known as the maximum capacity path problem. It is possible to adapt most shortest path algorithms to compute widest paths ...