Minimum Spanning Tree Algorithms
Explore different algorithms such as Kruskal's, Prim's, and Boruvka's for finding minimum spanning trees in graphs. Learn how they select safe edges and construct optimal spanning trees efficiently.
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Presentation Transcript
set S of edges is safe: there is an MST that contains S choose a component C in G[S] e min-weight edge crossing from C to its complement, then ? {?} is also safe
set S of edges is safe: there is an MST that contains S choose a component C in G[S] e min-weight edge crossing from C to its complement, then ? {?} is also safe Suppose not
set S of edges is safe: there is an MST that contains S choose a component C in G[S] e min-weight edge crossing from C to its complement, then ? {?} is also safe Suppose not
set S of edges is safe: there is an MST that contains S choose a component C in G[S] e min-weight edge crossing from C to its complement, then ? {?} is also safe Kruskal s algorithm: sort the edges in increasing order of weight Add an edge if it does not create a cycle with previously added edges, else reject it.
set S of edges is safe: there is an MST that contains S choose a component C in G[S] e min-weight edge crossing from C to its complement, then ? {?} is also safe Prim s algorithm: Start with a root node Each time chosen component = connected component of root node.
set S of edges is safe: there is an MST that contains S choose a component C in G[S] e min-weight edge crossing from C to its complement, then ? {?} is also safe Boruvka s algorithm: (assume distinct edge weights for simplicity) Each time, for each component choose the cheapest edge leaving it
