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Kruskal's algorithm is an approach for finding a minimum cost spanning tree in a weighted undirected graph by adding edges in ascending order of weight while ensuring no cycles are formed. The algorithm leverages a sorting mechanism and a union-find data structure to efficiently manage the merging of components representing tree structures. By applying a minimum separator lemma, Kruskal's algorithm guarantees an optimal solution through its method of edge selection and component merging.
Chapter 515 sections
Kruskal's algorithm is an approach for finding a minimum cost spanning tree in a weighted undirected graph by adding edges in ascending order of weight while ensuring no cycles are formed. The algorithm leverages a sorting mechanism and a union-find data structure to efficiently manage the merging of components representing tree structures. By applying a minimum separator lemma, Kruskal's algorithm guarantees an optimal solution through its method of edge selection and component merging.
A spanning tree of a graph that has the minimum possible total edge weight.
A greedy algorithm that finds a minimum spanning tree by sorting all edges and adding them only if they do not form a cycle.
A data structure that keeps track of elements partitioned into disjoint sets and supports efficient union and find operations.
A path in a graph that starts and ends at the same vertex without traversing any edge more than once.
A principle that states the smallest edge connecting two disjoint subsets of vertices must be part of every minimum spanning tree.
Total Questions
2
Estimated Time
4 min
Passing Score
70%
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