Oblivious integral routing for minimizing the quadratic polynomial cost

In this paper, we study the problem of minimizing the cost for a set of multicommodity traffic request ℛ in an undirected network G(V, E). Motivated by the energy efficiency of communication networks, we will focus on the case where the objective is to minimize ∑_e (l _e )². Here l_e represents the load on the edge e. For this problem, we propose an oblivious routing algorithm, whose decisions don't rely on the current traffic in the network. This feature enables our algorithm to be implemented efficiently in the high-capacity backbone networks to improve the energy efficiency of the entire network. The major difference between our work and the related oblivious routing algorithms is that our approach can satisfy the integral constraint, which does not allow splitting a traffic demand into fractional flows. We prove that with this constraint no oblivious routing algorithm can guarantee the competitive ratio bounded by o(|E|1/3). By contrast, our approach gives a competitive ratio of O(|E|1/2 log²|V|· log D), where D is the maximum demand of the traffic requests. This competitive ratio is tight up to O(|E|1/6 log²|V|· log D).