An Algorithm for the Cycled Shortest Path Problem

For a network with cycle, where at least one cycle exists, the Floyd- Warshall algorithm is probably the most used algorithm to determine he least cost path between every pair of nodes on this network, i.e. the solution for the shortest path problem with cycle. In this paper, a new algorithm for this problem which requires less computational effort than the Floyd-Warshall algorithm has been developed Furthermore, it can be shown that the basis of our algorithm is much easier to be learnt and understood which might be an advantage for educational puposes. A small example validates our algorithm and shows its implementation

A New Approach for Sensitivity Analysis in Network Flow Problems

This paper proposes a new approach to study the sensitivity analysis in the network ow problems, in particular, the minimum spanning tree and shortest path problems. In a sensitivity analysis, one looks for the amount of changes in the edges' weights, number of edges or number of vertices such that the optimal solution, i.e. the minimum spanning tree or shortest path does not change. We introduce a novel approach for this purpose, and develop associated mathematics. We discusstwo illustrative examples to show the applicability of the proposed approach