The traveling salesman problem is a well-known and important combinatorial optimization problem. The goal of this problem is to find the shortest Hamiltonian path that visits each city in a given list exactly once and then returns to the starting city. In this paper, for the first time, the shortest Hamiltonian path is achieved for 1071 Iranian cities. For solving this large-scale problem, tw...

We give an overview of models and efficient algorithms for optimally solving timetable information problems like “given a departure and an arrival station as well as a departure time, which is the connection that arrives as early as possible at the arrival station?” Two main approaches that transform the problems into shortest path problems are reviewed, including issues like the modeling of re...

One of user's queries from navigation service is to find the nearest facility in terms of time. The facility that is being questioned by the user as a destination may have a queuing service system (e.g. bank), which means that the cost function of the shortest path includes the waiting time at the destination as well as the travel time. This research conducts in the zone 1 of Mashhad with Bank ...

We investigate various problems related to circulant graphs { nding the shortest path between two vertices, nding the shortest loop, and computing the diameter. These problems are related to shortest vector problems in a special class of lattices. We give matching upper and lower bounds on the length of the shortest loop. We claim NPhardness results, and establish a worst-case/average-case conn...

The shortest path problem is among the most fundamental combinatorial optimization problems to answer reachability queries. It is hard to determine which vertices or edges are visited during shortest path traversals. In this paper, we provide an empirical analysis on how traversal algorithms behave on social networks. First, we compute the shortest paths between set of vertices. Each shortest p...

Globally shortest path problems have increasing demand due to voluminous datasets in applications like roadmaps, web search engines, mobile data sets, etc., Computing shortest path between nodes in a given directed graph is a very common problem. Among the various shortest path algorithms, Dijkstra’s shortest path algorithm [1] is said to have better performance with regard to run time than the...

In many fields of application, shortest path finding problems in very large graphs arise. Scenarios where large numbers of on-line queries for shortest paths have to be processed in real-time appear for example in traffic information systems. In such systems, the techniques considered to speed up the shortest path computation are usually based on precomputed information. One approach proposed o...

In this paper we consider the Origin-Destination (O-D) shortest path problem. We define the O-D shortest path problem as follows: We are given the set of nodes and edges in a network. Associated with each edge is a weight. In addition, we are given two subsets of the node set. One set is called the set of origin nodes and the other is called the set of destination nodes. The objective of the O-...

Shortest Path Problems are among the most studied network flow optimization problems, with interesting applications in various fields. One such field is transportation, where shortest path problems of different kinds need to be solved. Due to the nature of the application, transportation scientists need very flexible and efficient shortest path procedures, both from the running time point of vi...