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Dijkstra's algorithm (/ ˈ d aɪ k s t r ə z / DYKE-strəz) is an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, a road network. It was conceived by computer scientist Edsger W. Dijkstra in 1956 and published three years later.
By removing several elements at once a considerable speedup can be reached. But not all algorithms can use this kind of priority queue. Dijkstra's algorithm for example can not work on several nodes at once. The algorithm takes the node with the smallest distance from the priority queue and calculates new distances for all its neighbor nodes.
In computer science, smoothsort is a comparison-based sorting algorithm.A variant of heapsort, it was invented and published by Edsger Dijkstra in 1981. [1] Like heapsort, smoothsort is an in-place algorithm with an upper bound of O(n log n) operations (see big O notation), [2] but it is not a stable sort.
In Dijkstra's algorithm for the shortest path problem, vertices of a given weighted graph are extracted in increasing order by their distance from the starting vertex, and a priority queue is used to determine the closest remaining vertex to the starting vertex. Therefore, in this application, the priority queue operations are monotonic.
Chen et al. [11] examined priority queues specifically for use with Dijkstra's algorithm and concluded that in normal cases using a d-ary heap without decrease-key (instead duplicating nodes on the heap and ignoring redundant instances) resulted in better performance, despite the inferior theoretical performance guarantees.
The d-ary heap consists of an array of n items, each of which has a priority associated with it. These items may be viewed as the nodes in a complete d-ary tree, listed in breadth first traversal order: the item at position 0 of the array (using zero-based numbering) forms the root of the tree, the items at positions 1 through d are its children, the next d 2 items are its grandchildren, etc.
From a dynamic programming point of view, Dijkstra's algorithm for the shortest path problem is a successive approximation scheme that solves the dynamic programming functional equation for the shortest path problem by the Reaching method. [8] [9] [10] In fact, Dijkstra's explanation of the logic behind the algorithm, [11] namely Problem 2.
In computing, the producer-consumer problem (also known as the bounded-buffer problem) is a family of problems described by Edsger W. Dijkstra since 1965.. Dijkstra found the solution for the producer-consumer problem as he worked as a consultant for the Electrologica X1 and X8 computers: "The first use of producer-consumer was partly software, partly hardware: The component taking care of the ...