Formal method of synthesis of optimal topologies of computing systems based on projective description of graphs

TL;DR

This paper introduces a deterministic, graph projection-based method for synthesizing optimal interconnect topologies in computing systems, ensuring they meet specific property requirements through iterative restrictions.

Contribution

It presents a novel approach using graph projections for systematic topology synthesis, improving design accuracy and efficiency.

Findings

Method successfully synthesizes topologies with desired properties.

Projections help identify incompatible initial conditions.

Approach enhances systematic topology design process.

Abstract

A deterministic method for synthesizing the interconnect topologies optimized for the required properties is proposed. The method is based on the original description of graphs by projections, on establishing the bijective correspondence of the required properties and the projection properties of the initial graph, on postulating the corresponding restrictions of modified projections and on iteratively applying these restrictions to them either until the projection system is solved and the projections of the desired graph are obtained, or until its incompatibility with the given initial conditions is revealed.