Exact Wirelength of Embedding 3-Ary n-Cubes into certain Cylinders and Trees

TL;DR

This paper precisely calculates the wirelength for embedding 3-ary n-cubes into cylinders and specific trees, aiding optimal network design in parallel computing systems.

Contribution

It provides exact wirelength formulas for embedding 3-ary n-cubes into cylinders and certain trees, advancing network embedding theory.

Findings

Exact wirelength formulas derived for specific embeddings

Improved understanding of network embedding efficiency

Applications in designing efficient interconnection networks

Abstract

Graph embeddings play a significant role in the design and analysis of parallel algorithms. It is a mapping of the topological structure of a guest graph G into a host graph H, which is represented as a one-to-one mapping from the vertex set of the guest graph to the vertex set of the host graph. In multiprocessing systems the interconnection networks enhance the efficient communication between the components in the system. Obtaining minimum wirelength in embedding problems is significant in the designing of network and simulating one architecture by another. In this paper, we determine the wirelength of embedding 3-ary n-cubes into cylinders and certain trees.