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Topological sorting. In computer science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge (u,v) from vertex u to vertex v, u comes before v in the ordering. For instance, the vertices of the graph may represent tasks to be performed, and the edges may ...
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 ...
It is also possible to check whether a given directed graph is a DAG in linear time, either by attempting to find a topological ordering and then testing for each edge whether the resulting ordering is valid [18] or alternatively, for some topological sorting algorithms, by verifying that the algorithm successfully orders all the vertices ...
Pigeonhole sort. Pigeonhole sorting is a sorting algorithm that is suitable for sorting lists of elements where the number n of elements and the length N of the range of possible key values are approximately the same. [1] It requires O (n + N) time. It is similar to counting sort, but differs in that it "moves items twice: once to the bucket ...
Topological sorting. Finding 2-(edge or vertex)-connected components. Finding 3-(edge or vertex)-connected components. Finding the bridges of a graph. Generating words in order to plot the limit set of a group. Finding strongly connected components. Determining whether a species is closer to one species or another in a phylogenetic tree ...
Breadth-first search (BFS) is an algorithm for searching a tree data structure for a node that satisfies a given property. It starts at the tree root and explores all nodes at the present depth prior to moving on to the nodes at the next depth level. Extra memory, usually a queue, is needed to keep track of the child nodes that were encountered ...
Timsort is a stable sorting algorithm (order of elements with same key is kept) and strives to perform balanced merges (a merge thus merges runs of similar sizes). In order to achieve sorting stability, only consecutive runs are merged. Between two non-consecutive runs, there can be an element with the same key inside the runs.