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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 ...
This algorithm, also known as the "recursive backtracker" algorithm, is a randomized version of the depth-first search algorithm. Frequently implemented with a stack, this approach is one of the simplest ways to generate a maze using a computer. Consider the space for a maze being a large grid of cells (like a large chess board), each cell ...
In statistics, Kruskal's most influential work is his seminal contribution to the formulation of multidimensional scaling. In computer science, his best known work is Kruskal's algorithm for computing the minimal spanning tree (MST) of a weighted graph. The algorithm first orders the edges by weight and then proceeds through the ordered list ...
Reverse-delete algorithm. The reverse-delete algorithm is an algorithm in graph theory used to obtain a minimum spanning tree from a given connected, edge-weighted graph. It first appeared in Kruskal (1956), but it should not be confused with Kruskal's algorithm which appears in the same paper. If the graph is disconnected, this algorithm will ...
The version given here is that proven by Nash-Williams; Kruskal's formulation is somewhat stronger. All trees we consider are finite. Given a tree T with a root, and given vertices v, w, call w a successor of v if the unique path from the root to w contains v, and call w an immediate successor of v if additionally the path from v to w contains no other vertex.
O(n)[1] In computer science, a disjoint-set data structure, also called a union–find data structure or merge–find set, is a data structure that stores a collection of disjoint (non-overlapping) sets. Equivalently, it stores a partition of a set into disjoint subsets. It provides operations for adding new sets, merging sets (replacing them ...
For example, Kruskal's algorithm processes edges in turn, deciding whether to include the edge in the MST based on whether it would form a cycle with all previously chosen edges. Both Prim's algorithm and Kruskal's algorithm require processes to know the state of the whole graph, which is very difficult to discover in the message-passing model.
A third algorithm commonly in use is Kruskal's algorithm, which also takes O(m log n) time. A fourth algorithm, not as commonly used, is the reverse-delete algorithm, which is the reverse of Kruskal's algorithm. Its runtime is O(m log n (log log n) 3). All four of these are greedy algorithms.