Vyssotsky’s algorithm.Develop an implementation that computes the MST by applying the cycle property (see exercise 4.3.8) repeatedly: Add edges one at a time to a putative tree, deleting a maximum-weight edge on the cycle if one is formed. Note: This method has received less attention than the others that we consider because of the comparative difficulty of maintaining a data structure that supports efficient implementation of the “delete the maximum-weight edge on the cycle’’ operation.
Exercise4.3.8:
Prove the following, known as the cycle property:Given any cycle in an edge-weighted graph (all edge weights distinct), the edge of maximum weight in the cycle does not belong to the MST of the graph.
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