Information theoretic clustering: an approach to reduce user-tracking overheads in cellular networks

Tracking information about users in a cellular network may need to be clustered for reasons of efficient distributed storage, transmission limitations, network constraints etc., especially at the remote locations or edge servers. We present here an information theoretic framework for clustering user-tracking information. One would like to cluster the information in such a way that given the clustered information at a remote location, the number of bits required to reconstruct the complete information is minimum. This minimizes the overhead of transporting these extra description bits for reconstructing the complete information, whenever it is required at the remote location. Finding the optimal clustering to minimize the conditional description of an information has good bounds in the set of good solutions of the problem of partitioning n weights into k subsets such that the largest and the smallest subset sums is minimized. However, the latter problem of partitioning is an NP-complete problem but good heuristic algorithms exist which provide suboptimal solutions. We discuss some of these heuristic strategies to achieve suboptimal clusters, present a lower bound and an estimate of an upper bound to our optimal solution and show that the heuristic solution is quite close to the optimal solution