On a Clustering Partitioning Approach for Wireless Visible Light Communication Networks

Abstract

In this paper, we consider the problem of forming clusters of nodes in a wireless visible light communication (VLC for short) network. More precisely, let $G=(V,\ E)$ be a complete graph with a set of wireless devices $V$ (nodes) and a set of connection links $E$ (edges) representing the VLC network. We consider the problem of partitioning $k\leq \vert V\vert$ vertices into disjoint cliques of size of at most $\lfloor\frac{k}{t}\rfloor+1$ nodes where $t < k (k, t\in \mathbb{Z}_{+})$ such that the total power received plus the residual energy of each of the $k$ chosen nodes is maximized. Recall that clustering the sensor nodes of a network allows handling efficiently problems related to scalability, and routing, to name a few. In order to achieve the grouping task optimally, we propose integer linear and quadratic programming models based on classical combinatorial optimization problems from the literature. In order to compare our proposed models, we assume that every node in the network can communicate through a direct line of sight (DLOS) VLC channel. Our preliminary numerical results indicate that the quadratic model together with its linearized counterpart are the best ones as they allow to solve to optimality all tested instances in significantly less computational effort.