The Floyd-Warshall algorithm on graphs with negative cycles

The Floyd-Warshall Algorithm for Shortest Paths

The Floyd-Warshall algorithm [Flo62, Roy59, War62] is a classic dynamic programming algorithm to compute the length of all shortest paths between any two vertices in a graph (i.e. to solve the all-pairs shortest path problem, or APSP for short). Given a representation of the graph as a matrix of weights M , it computes another matrix M ′ which represents a graph with the same path lengths and c...

Using basis dependence distance vectors in the modified Floyd-Warshall algorithm

In this paper, we present a modified Floyd–Warshall algorithm, where the most time-consumingpart—calculating transitive closure describing self-dependences for each loop statement—is computed applying basis dependence distance vectors derived from all vectors describing self-dependences. We demonstrate that the presented approach reduces the transitive closure calculation time for parameterized...

A Parallel Recursive Approach for Solving All Pairs Shortest Path Problem on GPU using OpenCL

All-pairs shortest path problem(APSP) finds a large number of practical applications in real world. We owe to present a highly parallel and recursive solution for solving APSP problem based on Kleene’s algorithm. The proposed parallel approach for APSP is implemented using an open standard framework OpenCL which provides a development environment for utilizing massive parallel capabilities of M...

Transitive closure and metric inequality of weighted graphs: detecting protein interaction modules using cliques

We study transitivity properties of edge weights in complex networks. We show that enforcing transitivity leads to a transitivity inequality which is equivalent to ultra-metric inequality. This can be used to define transitive closure on weighted undirected graphs, which can be computed using a modified Floyd-Warshall algorithm. These new concepts are extended to dissimilarity graphs and triang...

A Faster All-Pairs Shortest Path Algorithm for Real-Weighted Sparse Graphs