Boost PC performance: How more available memory can improve productivity
My presentation all shortestpath
1. All-Pairs Shortest Path
Theory and Algorithms
Carlos Andres Theran Suarez
Program Mathematics and Scientific Computing
University of Puerto Rico
Carlos.theran@upr.edu
October – 2011
Mayaguez-Puerto Rico
Dr Marko Schütz
12. Outline
1. Present a dynamic programming algorithms based on
matrix multiplication to solve the problem.
2. Dynamic programming algorithms called Floyd-Warshall
algorithms.
3. Unlike the others algorithms, Johnson's algorithms used
adjacency-list representation of a graph.
27. Johnson's algorithm for sparse graphs.
• It is asymtoticaly better than repeated squaring of matrices
or the Floyd-Warshall algoritm.
• It use a subroutine both Dijkstra’s algorithm and Bellman-
Ford algorithm.
• Johnson's algorithm use the technique of reweighting.