Heuristics for Multiway Partitioning in Hexagonal Cellular Systems

Given a hexagonal mesh of base stations in cellular systems we consider the problem of nding a cover of disjoint clusters of base stations which generate multiple types of traac among themselves. The problem diiers from general graph partitioning problems in that it considers not only communication costs but also the underlying topology among base stations, such that base stations in a cluster are connected in their physical topology. The objective is to minimize the total communication cost for the entire system where inter-cluster communication is more expensive than intra-cluster communication for each type of traac. The problem is transformed into the dual based on a topology matrix and a relative cost matrix. We develop several heuristics for the dual. These heuristics produce optimal partitions with respect to the initial partition, based on the techniques of moving or interchanging the boundary nodes between adjacent clusters. The heuristics are compared and shown to behave quite well through experimental tests and analysis.