Visible light communication networks under ring and tree topology constraints

In this paper, we propose new mixed integer linear programming (MILP) models in order to maximize the total capacity of a wireless visible light communication (VLC) network subject to power and ring (or tree) topology constraints. VLC has appeared as a new promising technology as it allows to transmit data in significantly higher orders of magnitude than traditional radio frequency (RF) methods [7,11]. Moreover, it allows to establish wireless communications where RF technologies cannot operate in optimal conditions such as in airplanes, hospitals, nuclear areas, underground mining, underwater communications and disaster and traffic management, to name a few. Consequently, it is expected that most of the current existing protocols that use RF methods will incorporate this new technology in the near future. We propose exponential and compact polynomial formulations that we obtain from the classic traveling salesman and spanning tree problems in order to characterize the ring and tree topology constraints in our models. For each of the proposed models, we obtain robust formulations in the form of a MILP problem [6]. Finally, we adapt an exact iterative procedure to solve the exponential models to optimality [1]. For the deterministic and robust ring models, we solve instances with up to 500 and 300 nodes to optimality, respectively. Then, we further propose a new relaxed version of the algorithm that allows to compute tight near optimal solutions for all the exponential models with up to 500 nodes. In general, the two algorithms obtain solutions in significantly less CPU time when compared to the compact models.