Embedding Hierarchical Cubic Networks into k-Rooted Complete Binary Trees for Minimum Wirelength

Abstract

In recent years, the growth of data has promoted the development of parallel and distributed systems. Graph embedding is of great importance in improving parallel and distributed system performance. The quality of an embedding can be measured by many important metrics, and wirelength is one of the critical metrics related to communication performance and layout costs of physical systems. The hierarchical cubic network is a well-performing interconnection network and the [Formula: see text]-rooted complete binary tree is a data structure with a hierarchical relationship among its various elements in algorithms and programming. In this paper, we solve the problem of the embedding of hierarchical cubic networks into [Formula: see text]-rooted complete binary trees with minimum wirelength. We first study the optimal set of the hierarchical cubic network, and propose algorithms to give embedding [Formula: see text] which is an embedding scheme of hierarchical cubic networks into [Formula: see text]-rooted complete binary trees with minimum wirelength. Moreover, we give the exact minimum wirelength of this embedding. Finally, we conduct comparative experiments to evaluate the performance of embedding [Formula: see text].