This paper introduces weighted-BMP, a variant of the Bandwidth Minimization Problem (BMP), with a significant application in optimizing quantum emulation. Weighted-BMP optimizes particles ordering to reduce the emulation costs, by designing a particle interaction matrix where strong interactions are placed as close as possible to the diagonal. We formulate the problem using a Mixed Integer Linear Program (MILP) and solve it to optimality with a state-of-the-art solver. To strengthen our MILP model, we introduce symmetry-breaking inequalities and establish a lower bound. Through extensive numerical analysis, we examine the impacts of these enhancements on the solver’s performance. The introduced reinforcements result in an average CPU time reduction of 25.61%. Additionally, we conduct quantum emulations of realistic instances. Our numerical tests show that the weighted-BMP approach outperforms the Reverse Cuthill-McKee (RCM) algorithm—an efficient heuristic used for site ordering tasks in quantum emulation— achieving an average memory storage reduction of 24.48%. From an application standpoint, this study is the first to apply an exact optimization method, weighted-BMP, that considers interactions for site ordering in quantum emulation pre-processing, and shows its crucial role in cost reduction. From an algorithmic perspective, it contributes by introducing important reinforcements and lays the groundwork for future research on further enhancements, particularly on strengthening the weak linear relaxation of the MILP.

We model the network slice provisioning as an optimization problem including novel mapping and provisioning requirements rising with new radio and core function placement policies. We propose an open-access framework based on an MILP formulation that encompasses flexible functional splitting, with possibly different splitting for different slices and slice subnets, while taking into account different network sharing policies from 5G specifications. We also consider novel mapping and continuity constraints specific to the 5G architectures and beyond. We show by numerical simulations the impact of taking into full and partial consideration these peculiar novel technical constraints.

In this work, we model the network slice provisioning as an optimization problem including novel mapping and provisioning requirements rising with new 5G radio and core function placement policies. We propose an MILP-based formulation that joins different functional splitting strategies with different network function sharing policies and novel mapping continuity constraints from 5G specifications. We show by numerical simulations the impact of taking into full and partial consideration these peculiar sets of novel technical constraints.

International audience