Detect a negative cycle using the predecessor indices

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1. Show that if a network contains a negative cycle, the generic all-pairs label-correcting algorithm will never terminate.

2. Suppose that the Floyd-Warshall algorithm terminates after detecting the presence of a negative cycle. At this time, how would you detect a negative cycle using the predecessor indices?

3. In an all-pairs shortest path problem, suppose that several shortest paths connect node i and nodej. If we use the Floyd-Warshall algorithm to solve this problem, which path will the algorithm choose? Will this path be the one with the least number of arcs?

Reference no: EM131258352

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