Computer Science · Graph Algorithms
Which of the following accurately describes the precise mechanism by which the Bellman-Ford algorithm computes shortest paths and detects negative weight cycles in a weighted graph?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1It relies on a First-In-First-Out queue to process vertices in layers exactly |V|-1 times, automatically converting any detected negative edge weight into a positive value to prevent cycle formation.
- 2It computes strongly connected components through a sequence of |V|-1 edge relaxations and confirms a negative cycle when the overall sum of vertex in-degrees and out-degrees becomes negative.
- 3It iteratively expands the shortest paths by exploring vertices in non-decreasing order of distance using a min-heap, terminating the |V|-1 loops early if a negative edge weight is encountered.
- 4It computes shortest paths by sequentially relaxing all edges exactly |V|-1 times, and guarantees the detection of a negative weight cycle if a subsequent relaxation further reduces any vertex distance.✓
Correct answer
It computes shortest paths by sequentially relaxing all edges exactly |V|-1 times, and guarantees the detection of a negative weight cycle if a subsequent relaxation further reduces any vertex distance.
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