A New Variant of Benes Network: Its Topological Characterisation and Comparative Analysis

Abstract

The modern era is characterized by rapid advancements in technology, wherein the design and topology of interconnection networks play a pivotal role in enabling efficient communication systems. The analysis of topological and structural characteristics of interconnection networks, however, remains a challenging task. Graph theory facilitates this process by enabling analytical and efficient solutions through the use of numerical parameters known as topological descriptors. These descriptors have proven to be highly significant, with applications spanning computer science, chemistry, biology, and related domains. This paper deals with the evaluation of topological descriptors for an $n$-dimensional multistage interconnection network, namely the benes network, denoted as $BB(n)$. Additionally, a new variant of the interconnection network is derived from the benes network, called the augmented benes network and denoted as $BB^{*}(n)$. The topological descriptors for the derived network are also determined in this work. Furthermore, the benes network and the augmented benes network undergo a comparative analysis based on selected network parameters, which helps in understanding the efficiency of the newly derived network. A broadcasting algorithm for the augmented benes network is also presented.