Overview Statistic: PDF-Downloads (blue) and Frontdoor-Views (gray)

How Many Clues To Give? A Bilevel Formulation For The Minimum Sudoku Clue Problem

Please always quote using this URN: urn:nbn:de:0297-zib-90902
  • It has been shown that any 9 by 9 Sudoku puzzle must contain at least 17 clues to have a unique solution. This paper investigates the more specific question: given a particular completed Sudoku grid, what is the minimum number of clues in any puzzle whose unique solution is the given grid? We call this problem the Minimum Sudoku Clue Problem (MSCP). We formulate MSCP as a binary bilevel linear program, present a class of globally valid inequalities, and provide a computational study on 50 MSCP instances of 9 by 9 Sudoku grids. Using a general bilevel solver, we solve 95\% of instances to optimality, and show that the solution process benefits from the addition of a moderate amount of inequalities. Finally, we extend the proposed model to other combinatorial problems in which uniqueness of the solution is of interest.

Download full text files

Export metadata

Author:Gennesaret TjusilaORCiD, Mathieu BesanconORCiD, Mark TurnerORCiD, Thorsten KochORCiD
Document Type:ZIB-Report
MSC-Classification:90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90-08 Computational methods
Date of first Publication:2023/05/09
Series (Serial Number):ZIB-Report (23-15)
Accept ✔
Diese Webseite verwendet technisch erforderliche Session-Cookies. Durch die weitere Nutzung der Webseite stimmen Sie diesem zu. Unsere Datenschutzerklärung finden Sie hier.