The shortest path problem is among the most fundamental combinatorial optimization problems to answer reach-ability queries. A single pair shortest path computation using Dijkstra’s algorithm requires few seconds on a very large social network. Many traversal algorithms imply precomputed information to speed up the runtime query process. However, computing effective auxiliary data in a reasonab...

We consider brane cosmology studying the shortest null path on the brane for photons, and in the bulk for gravitons. We derive the differential equation for the shortest path in the bulk for a 1+4 cosmological metric. The time cost and the redshifts for photons and gravitons after traveling their respective path are compared. We consider some numerical solutions of the shortest path equation, a...

The quadratic shortest path (QSP) problem is to find a path from a node to another node in a given network such that the total cost includes two kinds of costs, say direct cost and interactive cost, is minimum. The direct cost is the cost associated with each arc and the interactive cost occurs when two arcs appear simultaneously in the shortest path. In this paper, the concept of the quadratic...

We address the determination of the second point-to-point shortest simple path in undirected networks. The effective reduced cost concept is introduced to compute the second best solution. This concept is used to prove that a path tree containing the second point-to-point shortest simple path is adjacent to any shortest path tree. Therefore, this result immediately implies a methods requiring O...

Let G be a graph with the usual shortest-path metric. A graph is δ-hyperbolic if for every geodesic triangle T , any side of T is contained in a δ-neighborhood of the union of the other two sides. A graph is chordal if every induced cycle has at most three edges. In this paper we study the relation between the hyperbolicity of the graph and some chordality properties which are natural generaliz...

The use of Geographic Information Systems has increased considerably since the eighties and nineties. As one of their most demanding applications we can mention shortest paths search. Several studies about shortest path search show the feasibility of using graphs for this purpose. Dijkstra's algorithm is one of the classic shortest path search algorithms. This algorithm is not well suited for s...

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 consider the problem of computing the optimal swap edges of a shortest-path tree. This problem arises in designing systems that offer point-of-failure shortest-path rerouting service in presence of a single link failure: if the shortest path is not affected by the failed link, then the message will be delivered through that path; otherwise, the system will guarantee that, when the message re...

We give a randomized parallel algorithm for computing single-source shortest paths in weighted digraphs. We show that the exact shortest-path problem can be efficiently reduced to solving a series of approximate shortest-path subproblems. Our algorithm for the approximate shortest-path problem is based on the technique used by Ullman and Yannakakis in a parallel algorithm for breadth-first sear...

In this paper it is introduced a biobjective ant algorithm for constructing low cost routing networks. The new algorithm is called the Distributed Pharaoh System (DPS). DPS is based on AntNet algorithm. The algorithm is using Pharaoh Ant System (PAS) with an extra-exploration phase and a 'no-entry' condition in order to improve the solutions for the Low Cost Network Routing problem. Additionall...