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The canonical application of topological sorting is in scheduling a sequence of jobs or tasks based on their dependencies.The jobs are represented by vertices, and there is an edge from x to y if job x must be completed before job y can be started (for example, when washing clothes, the washing machine must finish before we put the clothes in the dryer).
Graph. Worst-case performance. Tarjan's strongly connected components algorithm is an algorithm in graph theory for finding the strongly connected components (SCCs) of a directed graph. It runs in linear time, matching the time bound for alternative methods including Kosaraju's algorithm and the path-based strong component algorithm.
Kruskal's algorithm[1] finds a minimum spanning forest of an undirected edge-weighted graph. If the graph is connected, it finds a minimum spanning tree. It is a greedy algorithm that in each step adds to the forest the lowest-weight edge that will not form a cycle. [2] The key steps of the algorithm are sorting and the use of a disjoint-set ...
The Floyd–Warshall algorithm is an example of dynamic programming, and was published in its currently recognized form by Robert Floyd in 1962. [3] However, it is essentially the same as algorithms previously published by Bernard Roy in 1959 [4] and also by Stephen Warshall in 1962 [5] for finding the transitive closure of a graph, [6] and is closely related to Kleene's algorithm (published ...
Cocktail shaker sort, [1] also known as bidirectional bubble sort, [2] cocktail sort, shaker sort (which can also refer to a variant of selection sort), ripple sort, shuffle sort, [3] or shuttle sort, is an extension of bubble sort. The algorithm extends bubble sort by operating in two directions. While it improves on bubble sort by more ...
In computational geometry, a sweep line algorithm or plane sweep algorithm is an algorithmic paradigm that uses a conceptual sweep line or sweep surface to solve various problems in Euclidean space. It is one of the critical techniques in computational geometry. The idea behind algorithms of this type is to imagine that a line (often a vertical ...
The examples use the poset (({,,}),) consisting of the set of all subsets of a three-element set {,,}, ordered by set inclusion (see Fig. 1). a is related to b when a ≤ b . This does not imply that b is also related to a , because the relation need not be symmetric .
Borůvka's algorithm is a greedy algorithm for finding a minimum spanning tree in a graph, or a minimum spanning forest in the case of a graph that is not connected. It was first published in 1926 by Otakar Borůvka as a method of constructing an efficient electricity network for Moravia. [1][2][3] The algorithm was rediscovered by Choquet in ...