The elementary shortest path problem with resource constraints (ESPPRC) is a widely used modeling tool in formulating vehicle routing and crew scheduling applications, see e.g. [3]. The ESPPRC consists of finding shortest paths from a source to all other nodes of a network that do not contain any cycles, i.e. duplicate nodes. The ESPPRC occurs as a subproblem of an enclosing problem and is used...

In this article we present an algorithm for converting a network problem with several sources and several sinks including several transfer nodes and condition of supplying the demand of any sink from a particular source to the transportation problem.  Towards this end, and considering the very special structure of transportation algorithm, after implementing the shortest path algorithm or ...

Shortest path computation is a fundamental problem in road networks with various applications in research and industry. However, returning only the shortest path is often not satisfying. Users might also be interested in alternative paths that are slightly longer but have other desired properties, e.g., less frequent traffic congestion. In this paper, we study alternative routing and, in partic...

The shortest path problem in the time dependent network is an important extension of the classical shortest path problem and has been widely applied in real life. It is known as nonlinear and NP-hard. Therefore, the algorithms of the classical shortest path are incapable to solve this problem. In this paper, the models of the shortest path problem in the time dependent network are formulated an...

The first work on the network optimisation problem of rankingK shortest paths, K ∈ IN, appeared in 1959, more or less simultaneously with the first papers on the shortest path problem. Since then the particular problem (when K = 1) has merited much more attention than its generalisation. Nevertheless, several titles are included on the very complete bibliography about theK shortest paths proble...

An algorithm is presented for computing geodesic furthest neighbors for all the vertices of a simple polygon, where geodesic denotes the fact that distance between two points of the polygon is defined as the length of an Euclidean shortest path connecting them within the polygon. The algorithm runs in O(n log n) time and uses O(n) space; n being the number of vertices of the polygon. As a corol...