Search results
Results from the WOW.Com Content Network
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.
In graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph.A path is called simple if it does not have any repeated vertices; the length of a path may either be measured by its number of edges, or (in weighted graphs) by the sum of the weights of its edges.
Dijkstra's algorithm finds the shortest path from a given source node to every other node. [7]: 196–206 It can be used to find the shortest path to a specific destination node, by terminating the algorithm after determining the shortest path to the destination node. For example, if the nodes of the graph represent cities, and the costs of ...
Prune and search is a method of solving optimization problems suggested by Nimrod Megiddo in 1983. [1]The basic idea of the method is a recursive procedure in which at each step the input size is reduced ("pruned") by a constant factor 0 < p < 1.
The algorithm can be made much more effective by first sorting the list of items into decreasing order (sometimes known as the first-fit decreasing algorithm), although this still does not guarantee an optimal solution and for longer lists may increase the running time of the algorithm. It is known, however, that there always exists at least ...
In fact in order to answer a level ancestor query, the algorithm needs to jump from a path to another until it reaches the root and there could be Θ(√ n) of such paths on a leaf-to-root path. This leads us to an algorithm that can pre-process the tree in O(n) time and answers queries in O(√ n). In order to reach the optimal query time, we ...
Trie data structures are commonly used in predictive text or autocomplete dictionaries, and approximate matching algorithms. [11] Tries enable faster searches, occupy less space, especially when the set contains large number of short strings, thus used in spell checking, hyphenation applications and longest prefix match algorithms.
There are classical sequential algorithms which solve this problem, such as Dijkstra's algorithm. In this article, however, we present two parallel algorithms solving this problem. Another variation of the problem is the all-pairs-shortest-paths (APSP) problem, which also has parallel approaches: Parallel all-pairs shortest path algorithm.