Shortest Path Problem (SSP)

Shortest Path Problem (SSP)

graph_theory graph_algorithm graph_problem path_problem optimization_problem combinatorial_optimization graph_distance discrete_mathematics
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🔥 All-Pairs Shortest Path → All-pairs shortest path leverages single-source shortest path routines: run SSSP from every vertex (e.g., repeated Dijkstra for nonnegative weights, Bellman–Ford for negative edges) or use Johnson’s algorithm (reweighting + Dijkstra). Even Floyd–Warshall computes the same shortest-path notion; understanding SSSP is required to choose and implement these methods correctly.
🔥 Single-Source Shortest Path → Single-source shortest path refines the general shortest path problem to computing minimum-cost paths from one fixed source to all nodes, applying the same cost model and constraints and selecting suitable algorithms (e.g., BFS for unweighted, Dijkstra for positive weights, Bellman–Ford for negative edges).
🔥 Single-Pair Shortest Path → Single-pair shortest path depends on the general shortest-path formulation (cost models, edge weights) and the standard algorithms (BFS, Dijkstra, Bellman-Ford, A*) specialized to a single source-target query.
🌟 Dijkstra Algorithm →
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Floyd-Warshall Algorithm →
Bellman-Ford Algorithm →
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