Module: All pairs shortest paths

Johnson’s algorithm, Floyd-Warshall algorithm, dynamic programming for dense graphs, transitive closure

Learning Outcomes

Understand all pairs shortest paths

Understand when, why, and how to use all pairs shortest paths.

Readings

Introduction to all pairs shortest paths

Introduction.

Screencast Suthers 10 min

Johnson's algorithm for all pairs shortest paths

Johnson’s algorithm

Screencast Suthers 24 min

Floyd-Warshall algorithm for all pairs shortest paths

Floyd-Warshall’s algorithm

Screencast Suthers 20 min

CLRS 25 - All Pairs Shortest Paths

Shortest paths and matrix multiplication, Floyd-Warshall algorithm, Johnson’s algorithm for sparse graphs

Textbook 22 pages

Notes on all pairs shortest paths

All pairs shortest paths problem, using single source algorithms, Johnson’s bright idea, Floyd-Warshall: dynamic programming for dense graphs, transitive closure

Notes