Embedding algorithm of spined cube into grid structure and its wirelength computation

Abstract

In the field of data science, graph embedding is a vital tool to simulate, visualize and design a parallel architecture. The binary cube is one of the most desirable and reliable network-based architecture with high performance, yet many variations have been proposed on the links of the cube to enhance its computational power. The spined cube is a new efficient variant of the binary cube with a smaller diameter and preserves the advantageous properties of the original cube. Grid embedding is accustomed to study simulation capacity of a parallel and distributed computer system and conjointly designs its VLSI layout. In this paper, we propose an algorithm to embed the spined cube into a grid and compute the minimum wirelength over all possible embeddings using the edge congestion technique.