The time delay of a long-distance call can be determined by multiplying a small fixed constant by the number of communication links on the telephone network between the caller and callee. Suppose...
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1. Let G be a graph with n vertices and m edges such that all the edge weights in G are integers in the range [1,n]. Give an algorithm for finding a minimum spanning tree for G in O(mlog∗ n) time.2....
Tamarindo University and many other schools worldwide are doing a joint project on multimedia. A computer network is built to connect these schools using communication links that form a tree. The...
Say that an n-vertex directed acyclic graph is compact if there is some way of numbering the vertices of with the integers from 0 to n−1 such that contains the edge (i, j) if and only if i...
1. Let be a weighted directed graph with n vertices. Design a variation of FloydWarshall’s algorithm for computing the lengths of the shortest paths from each vertex to every other vertex in O(n3)...
An independent set of an undirected graph G = (V,E) is a subset I of V such that no two vertices in I are adjacent. That is, if u and v are in I, then (u,v) is not in E. A maximal independent set M...
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