An efficient way to represent the processors and their connections in omega networks

The understanding of the structure of a network can be enhanced efficiently with distance-reliant parameters. The metric dimension is one such parameter with numerous variations and a rich source of literature. The subject of our study pertains to the metric dimension and a few of its variants for a broadly used interconnection network-omega network. Omega networks provide a structured and scalable interconnect solution for distributed memory architectures. In large-scale data centers where massive amounts of data are processed and analyzed, omega networks are used in the network infrastructure to interconnect servers and storage systems. The key feature of omega networks is their ability to provide multiple disjoint paths between any pair of nodes in the network. This characteristic helps reduce congestion and improve overall system performance, especially in large-scale parallel computing environments where data communication is a critical factor. Along with metric dimension, we provide the exact values of edge metric dimension, fault-tolerant metric and edge metric dimensions for this widely known network. We also compare these parameters with those of other predominant interconnection networks, such as the butterfly, Beneš, and fractal cubic networks, and we observe that the omega network has significantly lower values for these parameters compared to the other networks.