Integer Programming Approach to the Data Traffic Paths Recovering Problem

In this paper, we propose a novel approach to recovering path relationships in communication networks. The path relationship is one of the key input data which is necessary for network operation and maintenance. We have a continuous network transformation, upgrades, expansions, service allocations, thus the network physical topology and paths relationship are permanently changing with high frequency. Our approach is aimed at recovering the path relationships through flow information of each arc in the network. Getting the flow information is not a big technical problem and its control is included in the basic toolbox for network monitoring. We consider two scenarios which lead us to integer linear programs. The both of them minimize the flow deviation, where in the first one we look for a directed spanning tree (r-arborescence) and, in the second one—more general origin/destination paths (OD-paths). We propose mixed integer linear programming formulations for both problems. Their feature is that they contain the non-polynomial number of constraints which are considered implicitly by the cutting planes approach. The preliminary computation results showed that the large-scale instances of the first scenario can easily be solved. At the same time, the optimal solutions of second scenario problems can be found only on small- and medium-size instances, which inspires for the further research.