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Kruskal's 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 ...
Institutions. University of Michigan. Bell Labs. Thesis. The Theory of Well-Partially-Ordered Sets (1954) Doctoral advisors. Roger Lyndon. Paul Erdős. Joseph Bernard Kruskal, Jr. (/ ˈkrʌskəl /; January 29, 1928 – September 19, 2010) was an American mathematician, statistician, computer scientist and psychometrician.
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.
An animation of generating a 30 by 20 maze using Kruskal's algorithm. This algorithm is a randomized version of Kruskal's algorithm. Create a list of all walls, and create a set for each cell, each containing just that one cell. For each wall, in some random order: If the cells divided by this wall belong to distinct sets: Remove the current wall.
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.
The Kruskal count[1][2] (also known as Kruskal's principle, [3][4][5][6][7] Dynkin–Kruskal count, [8] Dynkin's counting trick, [9] Dynkin's card trick, [10][11][12][13] coupling card trick[14][15][16] or shift coupling[10][11][12][13]) is a probabilistic concept originally demonstrated by the Russian mathematician Evgenii Borisovich Dynkin in ...
The naive algorithm for single linkage clustering is essentially the same as Kruskal's algorithm for minimum spanning trees. However, in single linkage clustering, the order in which clusters are formed is important, while for minimum spanning trees what matters is the set of pairs of points that form distances chosen by the algorithm.