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)...
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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...
George claims he has a fast way to do path compression in a partition structure, starting at a position p. He puts p into a list L, and starts following parent pointers. Each time he encounters a...
1. Give an example of an n-vertex simple graph G that causes Dijkstra’s algorithm to run in Ω(n2 logn) time when its implemented with a heap.2. Give an example of a weighted directed graph with...
1. Let G be an undirected graph with n vertices and m edges. Describe an O(n+m)- time algorithm for traversing each edge of G exactly once in each direction.2. Implement an algorithm that returns a...
Our implementation of shortestPathLengths in Code Fragment 14.13 relies on use of “infinity” as a numeric value, to represent the distance bound for vertices that are not (yet) known to be reachable...
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