Partitioning technique for transforming perfect binary trees into single-row networks

Abstract

Many problems in science and engineering can be simplified into the form of a perfect binary tree. This paper discusses our study entitled Perfect Binary Tree Sequence (PBTS) which transforms a perfect binary tree into the single-row network. The transformation is necessary in applications such as in the assignment of telephone channels to caller–receiver pairs roaming in cells in a cellular network on real-time basis. In this application, each caller and receiver in a call forms a node, while their pair connection forms the edge. A specific case of the graph in the form of a binary tree is then transformed into its corresponding single-row network for assigning the channels to the caller–receiver pairs. PBTS starts with the formation of the spine from a perfect binary tree through the insertion mechanism, and this leads to the expansion of the spine into one or more zones in the single-row network. This is followed by the formation of terminals and intervals for optimal transformation into the nets of the single-row network using our earlier method called ESSR. The numerical experiment results support our hypothesis that PBTS transforms the tree into its single-row network efficiently.