The shortest path problem (SPP) is one of the most important combinatorial optimization problems in graph theory due to its various applications. The uncertainty existing in the real world problems makes it difficult to determine the arc lengths exactly. The fuzzy set is one of the popular tools to represent and handle uncertainty in information due to incompleteness or inexactness. In most cas...

A new approach to computing traveltimes and ray paths by solving the shortest path problem is presented. The technique is based on a partitioning of the shortest path optimization problem into smaller problems. We recursively evaluate the solution on expanding wavefronts instead of finding the global shortest paths from the source. To solve the local minimization, we apply a modified version of...

We consider a constrained shortest path problem with the possibility to refill the resource at certain nodes. This problem is motivated by routing electric vehicles with a comparatively short cruising range due to the limited battery capacity. Thus, for longer distances the battery has to be recharged on the way. Furthermore, electric vehicles can recuperate energy during downhill drive. We ext...

Let G = (V,E) (|V | = n and |E| = m) be an undirected graph with positive edge weights. Let PG(s, t) be a shortest s− t path in G. Let l be the number of edges in PG(s, t). The Edge Replacement Path problem is to compute a shortest s− t path in G\{e}, for every edge e in PG(s, t). The Node Replacement Path problem is to compute a shortest s− t path in G\{v}, for every vertex v in PG(s, t). In t...

Due to the process of network convergence, the variety of types of traffic transmitted over a single medium increases steeply. This phenomenon can be handled by the existing networking structure although the protocols that are used and, especially, the underlying routing protocols need to be improved. The problem of finding the shortest path on the Internet can no longer be easily defined as th...

in this paper, shortest path design problem (spdp) in which the path is incident to all cells is considered. the bi-directional path is one of the known types of configuration of networks for automated guided vehi-cles (agv).to solve this problem, two algorithms are developed. for each algorithm an integer linear pro-gramming (ilp) is determined. the objective functions of both algorithms are t...

Shortest path algorithms are required by several transportation applications; furthermore, the shortest path computation in these applications can account for a large percentage of the total execution time. Since these algorithms are very computationally intense, parallel processing can provide the compute power and memory required to solve large problems quickly. Therefore, good parallel short...

We present optimal parallel algorithms that run in O(p n) time on a p n p n mesh-connected computer for a number of fundamental problems concerning visibility and distance properties inside a simple polygon. These include computing shortest paths, shortest path trees, shortest path partitions, all-farthest neighbors (both internal and external), the visibility polygon of a point, the weak visib...