Design a variation of floyd-warshalls algorithm

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Reference no: EM131841749

Problem

1. Let G^→ be a weighted digraph with n vertices. Design a variation of Floyd-Warshall's algorithm for computing the lengths of the shortest paths from each vertex to every other vertex in O(n³) time.

2. A graph G is bipartite if its vertices can be partitioned into two sets X and Y such that every edge in G has one end vertex in X and the other in Y. Design and analyze an efficient algorithm for determining if an undirected graph G is bipartite (without knowing the sets X and Y in advance).

Reference no: EM131841749

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