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Prim's algorithm has many applications, such as in the generation of this maze, which applies Prim's algorithm to a randomly weighted grid graph. The time complexity of Prim's algorithm depends on the data structures used for the graph and for ordering the edges by weight, which can be done using a priority queue. The following table shows the ...
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 ]
Similarly to Prim's algorithm there are components in Kruskal's approach that can not be parallelised in its classical variant. For example, determining whether or not two vertices are in the same subtree is difficult to parallelise, as two union operations might attempt to join the same subtrees at the same time.
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.
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.
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 find a minimum spanning ...
A minimum spanning tree of a weighted planar graph.Finding a minimum spanning tree is a common problem involving combinatorial optimization. Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, [1] where the set of feasible solutions is discrete or can be reduced to a discrete set.
As stated above, the complexity of finding a convex hull as a function of the input size n is lower bounded by Ω(n log n). However, the complexity of some convex hull algorithms can be characterized in terms of both input size n and the output size h (the number of points in the hull). Such algorithms are called output-sensitive algorithms.