Bellman–Ford algorithm

Abstract: Deals with the problem of managing quantitative temporal networks without disjunctive constraints. This problem is known as the "simple temporal problem". Dynamic management algorithms are considered to be coupled with incremental constraint posting approaches for planning and scheduling. A basic algorithm for incremental propagation of a new time constraint is presented which is a modification of the Bellman-Ford algorithm for the single-source shortest-path problem. For this algorithm, a sufficient condition for inconsistency is given, based on cycle detection in the shortest-paths graph. Moreover, the problem of constraint retraction from a consistent situation is considered, and properties for repropagating the network locally are exploited. Some experiments are also presented that show the usefulness of these properties.

Abstract: Finding the shortest paths from a single source to all other vertices is a common problem in graph analysis. The Bellman-Ford's algorithm is the solution that solves such a single-source shortest path (SSSP) problem and better applies to be parallelized for many-core architectures. Nevertheless, the high degree of parallelism is guaranteed at the cost of low work efficiency, which, compared to similar algorithms in literature (e.g., Dijkstra's) involves much more redundant work and a consequent waste of power consumption. This article presents a parallel implementation of the Bellman-Ford algorithm that exploits the architectural characteristics of recent GPU architectures (i.e., NVIDIA Kepler, Maxwell) to improve both performance and work efficiency. The article presents different optimizations to the implementation, which are oriented both to the algorithm and to the architecture. The experimental results show that the proposed implementation provides an average speedup of $5 \times$ higher than the existing most efficient parallel implementations for SSSP, that it works on graphs where those implementations cannot work or are inefficient (e.g., graphs with negative weight edges, sparse graphs), and that it sensibly reduces the redundant work caused by the parallelization process.

Abstract: A control-plane architecture for supporting advance reservation of dedicated bandwidth channels on a switched network infrastructure is described including the front-end web interface, user and token management scheme, bandwidth scheduler, and signaling daemon. A path computation algorithm for bandwidth scheduling is proposed based on an extension of Bellman-Ford algorithm to an algebraic structure on sequences of disjoint non-negative real intervals. An implementation of this architecture for UltraScience Net is briefly described.