Optimal Routing in Multi-Service Networks

Abstract

In this paper we consider Resource Constrained Shortest Path problem (RCSP). This problem is NP-hard extension of the well-known shortest path problem in the directed graph $\boldsymbol{G}=(\boldsymbol{V},\boldsymbol{E})$ . In RCSP problem each arc $\boldsymbol{e}$ from $\boldsymbol{E}$ has a cost $\boldsymbol{w}(\boldsymbol{e})$ and additional weight functions $\boldsymbol{w_{r}}(\boldsymbol{e})$ which specifying its requirements from a finite set of resource. For each resource $\boldsymbol{r}$ defined restriction $\boldsymbol{W_{r}}$ . Path between given $\boldsymbol{s}$ and $\boldsymbol{d}$ vertices is feasible if it resource consumption not exceed restrictions $\boldsymbol{W_{r}}$ . It is required to find feasible shortest $(\boldsymbol{s},\boldsymbol{d})$ -path. Such problem allows to model multi-service networks and to search optimal route between two certain vertices. Nowadays multi-service networks grow quickly this increases either node and services count. In such network a hundred thousand nodes may be. Three classes of methods have been proposed to solve RCSP problem: path-ranking methods, node-labeling methods and methods that uses Lagrangian relaxation. The first two classes of methods are based on the graph-theoretic formulation of the problem. Last class uses integer linear programming formulation. Most of these methods work slowly on networks of large dimension. In this paper we propose two heuristic algorithms for approximate solving RCSP problem on big graphs. First algorithm is modification of the famous Dijkstra's algorithm with additional labels. Second algorithm adds potential functions and landmarks to the first, that allow significant accelerate Dijkstra's algorithm on big graphs. We provide computational experiments that show efficiency of proposed algorithms on graphs with number of nodes up to three hundred thousand.