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A demo for Union-Find when using Kruskal's algorithm to find minimum spanning tree. Disjoint-set data structures model the partitioning of a set, for example to keep track of the connected components of an undirected graph. This model can then be used to determine whether two vertices belong to the same component, or whether adding an edge ...
The simplest version of the algorithm uses the union-find data structure, which unlike other lowest common ancestor data structures can take more than constant time per operation when the number of pairs of nodes is similar in magnitude to the number of nodes. A later refinement by Gabow & Tarjan (1983) speeds the algorithm up to linear time.
Union, a datum which may be one of a set of types Tagged union (also called a variant , discriminated union or sum type ), a union with a tag specifying which type the data is Abstract data types
The algorithm continues this way, and creates new region labels whenever necessary. The key to a fast algorithm, however, is how this merging is done. This algorithm uses the union-find data structure which provides excellent performance for keeping track of equivalence relationships. [14]
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In this tree, the lowest common ancestor of the nodes x and y is marked in dark green. Other common ancestors are shown in light green. In graph theory and computer science, the lowest common ancestor (LCA) (also called least common ancestor) of two nodes v and w in a tree or directed acyclic graph (DAG) T is the lowest (i.e. deepest) node that has both v and w as descendants, where we define ...
7.2.3. Generating inequivalent patterns (includes discussion of Pólya enumeration theorem) (see "Techniques for Isomorph Rejection", chapter 4 of "Classification Algorithms for Codes and Designs" by Kaski and Östergård) 7.3. Shortest paths; 7.4. Graph algorithms. 7.4.1. Components and traversal 7.4.1.1. Union-find algorithms; 7.4.1.2. Depth ...
The Hoshen–Kopelman algorithm is a simple and efficient algorithm for labeling clusters on a grid, where the grid is a regular network of cells, with the cells being either occupied or unoccupied. This algorithm is based on a well-known union-finding algorithm. [1]