Duality for Sudoku

TL;DR

This paper introduces a mathematical duality framework for Sudoku, establishing a primal-dual model pair and proving weak and strong duality properties to deepen understanding of the puzzle's structure.

Contribution

It presents the first formal primal and dual models for Sudoku, along with duality relations and optimization formulations.

Findings

Duality relation between primal and dual Sudoku models

Weak and strong duality properties established

Optimization problems formulated for Sudoku

Abstract

We consider a mathematical model for the classical Sudoku puzzle, which we call the primal problem and introduce a corresponding dual problem. Both problems are constraint satisfaction models and a duality relation between them is proved. Based on these models, we introduce a primal and a dual optimization problem and show weak and strong duality properties.