A topology-based algorithm for the isomorphism check of 2-level Orthogonal Arrays

TL;DR

This paper presents a novel topology-based algorithm using Topological Data Analysis to determine isomorphism of 2-level Orthogonal Arrays by comparing their persistence diagrams and Wasserstein distances.

Contribution

It introduces a new TDA-based method for OA isomorphism checking, linking persistence diagrams with design equivalence.

Findings

Persistence diagrams effectively distinguish non-isomorphic OAs.

Wasserstein distance correlates with OA isomorphism status.

The method offers a new topological perspective for combinatorial design analysis.

Abstract

We introduce a construction and an algorithm, both based on Topological Data Analysis (TDA), to tackle the problem of the isomorphism check of Orthogonal Arrays (OAs). Specifically, we associate to any binary OA a persistence diagram, one of the main tools in TDA, and explore how the Wasserstein distance between persistence diagrams can be used to inform whether two designs are isomorphic.