Solving Single-digit Sudoku Subproblems

TL;DR

This paper demonstrates that single-digit Nishio subproblems in nxn Sudoku can be solved more efficiently than previous methods, and establishes that single-digit deduction in Sudoku is NP-hard.

Contribution

It introduces a faster algorithm for solving Nishio subproblems and proves the NP-hardness of single-digit deduction in Sudoku.

Findings

Nishio subproblems can be solved in time o(2^n)

Single-digit deduction in Sudoku is NP-hard

Improved computational complexity over previous methods

Abstract

We show that single-digit "Nishio" subproblems in nxn Sudoku puzzles may be solved in time o(2^n), faster than previous solutions such as the pattern overlay method. We also show that single-digit deduction in Sudoku is NP-hard.