All-pairs shortest-paths computation in the presence of negative cycles

The Floyd-Warshall algorithm on graphs with negative cycles

The Floyd-Warshall algorithm is a simple and widely used algorithm to compute shortest paths between all pairs of vertices in an edge weighted directed graph. It can also be used to detect the presence of negative cycles. We will show that for this task many existing implementations of the Floyd-Warshall algorithm will fail because exponentially large numbers can appear during its execution.

All Pairs Shortest Paths Algorithms

Given a communication network or a road network one of the most natural algorithmic question is how to determine the shortest path from one point to another. In this paper we deal with one of the most fundamental problems of Graph Theory, the All Pairs Shortest Path (APSP) problem. We study three algorithms namely The FloydWarshall algorithm, APSP via Matrix Multiplication and the Johnson’s alg...

Fast Shortest Paths Algorithms in the Presence of Few Negative Arcs

The shortest paths problem on weighted directed graphs is one of the basic network optimization problems. Its importance is mainly due to its applications in various areas, such as communication and transportation. Given a source node s in a weighted directed graph G, with n nodes and m arcs, the single-source shortest path problem (SSSP, for short) from s is the problem of finding the minimum ...

Recursive Cut and Stitch: Fast All-Pairs Shortest Paths Computation for Subset of Nodes

We present a practical algorithm for computing all pairs shortest paths for subset of nodes on road networks. It provides an important improvement for applications such as traffic analysis, where recomputation of shortest paths is the most expensive step that has to be repeated many times. We propose an algorithm that recursively cuts the graph until pieces are small enough to compute shortest ...

Synchronisation-Efficient Parallel All-Pairs Shortest Paths Computation