There Is No 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem via Hitting Set Enumeration

@article{McGuire2014ThereIN,
  title={There Is No 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem via Hitting Set Enumeration},
  author={Gary McGuire and Bastian Tugemann and Gilles Civario},
  journal={Experimental Mathematics},
  year={2014},
  volume={23},
  pages={190 - 217}
}
The sudoku minimum number of clues problem is the following question: what is the smallest number of clues that a sudoku puzzle can have? For several years it had been conjectured that the answer is 17. We have performed an exhaustive computer search for 16-clue sudoku puzzles and did not find any, thus proving that the answer is indeed 17. In this article we describe our method and the actual search. As a part of this project, we developed a novel way to enumerate hitting sets. The hitting set… 
Exact Method for Generating Strategy-Solvable Sudoku Clues
TLDR
A rigorous framework is introduced to discuss solvability for Sudoku instances with respect to strategies, and an exact method for determining Sudoku clues for a given set of clue positions that is solvable with aGiven set of strategies is proposed.
Minuet: A method to solve Sudoku puzzles by hand
TLDR
It is conjectured that this method can solve all well-posed 9 x 9 puzzles and is based on a new system of markings and a new way of simplifying the puzzles that can be easily carried out by hand--or by computer.
Approaching the minimum number of clues Sudoku problem via the polynomial method
Determining the minimum number of clues that must be present in a Sudoku puzzle in order to uniquely complete the puzzle is known as the minimum number of clues problem. For a 9 9 Sudoku board, it
Approaching the minimum number of clues Sudoku problem via the polynomial method
Determining the minimum number of clues that must be present in a Sudoku puzzle in order to uniquely complete the puzzle is known as the minimum number of clues problem. For a 9× 9 Sudoku board, it
A new algorithm for enumerating all possible Sudoku squares
TLDR
The aim of this paper is to propose a new algorithm for enumerating all possible Sudoku squares of size n2 based on the concepts of permutations derived from n2 × n2 S-permutation matrices termed as S- permutations, which is more systematic and better in terms of computational efficiency.
Fog of Search Resolver for Minimum Remaining Values Strategic Colouring of Graph
TLDR
The paper relates the cause of search plateaus in MRV to ‘Fog of Search’ (FoS), and consequently proposes improvements to MRVTo resolve the situation, the improved MRV+ generates a secondary heuristics value called the Contribution Number, and employs it to resolve a FoS.
A Hybrid alldifferent-Tabu Search Algorithm for Solving Sudoku Puzzles
TLDR
This paper proposes a new hybrid algorithm that smartly combines a classic tabu search procedure with the alldifferent global constraint from the constraint programming world, known to be efficient for domain filtering in the presence of constraints that must be pairwise different.
Sudoku Solver
TLDR
The design, implementation, and evaluation of an android Sudoku solving app is discussed, which allows users to solve a puzzle using pencil marks, while allowing them to request hints which are generated based on an extensive set on human solving techniques.
Efficiency of the hybrid AC3-tabu search algorithm for solving Sudoku puzzles
TLDR
The results show that the hybrid AC3-tabu search algorithm is less efficient than the two other algorithms, and that there seems to be a correlation between the number of clues and the solving time for the algorithm.
Sudoku Rectangle Completion
Over the last decade, Sudoku, a combinatorial number-placement puzzle, has become a favorite pastimes of many all around the world. In this puzzle, the task is to complete a partially filled $9
...
...

References

SHOWING 1-10 OF 82 REFERENCES
An Efficient Approach to Solving the Minimum Sudoku Problem
TLDR
A new algorithm, named disjoint minimal unavoidable set (DMUS) algorithm, is designed to help solve the minimum Sudoku problem more efficiently and the performance was greatly improved by a factor of 128.67.
Solving the Minimum Sudoku Poblem
  • Hung-Hsuan Lin, I-Chen Wu
  • Computer Science
    2010 International Conference on Technologies and Applications of Artificial Intelligence
  • 2010
TLDR
A new algorithm, named a disjoint minimal unavoidable set (DMUS) algorithm, is proposed to help solve the minimum Sudoku problem and it becomes feasible and optimistic to solve this program using a volunteer computing system, such as BOINC.
Taking Sudoku Seriously
TLDR
A Sudoku puzzle is a partially filled-in Sudoku board that can be completed in exactly one way, and all well-made Sudoku puzzles have this property.
Taking Sudoku Seriously: The Math Behind the World's Most Popular Pencil Puzzle
1. Playing the Game Mathematics as Applied Puzzle-Solving 2. Latin Squares What Do Mathematicians Do? 3. Greco-Latin Squares The Problem of the Thirty-Six Officers 4. Counting It's Harder Than it
Minimal number of clues for Sudokus
  • Christoph Lass
  • Mathematics
    Central European Journal of Computer Science
  • 2012
TLDR
A universal scheme for calculating the minimal number of clues needed for a generalized Sudoku to be uniquely solvable is presented by using equivalence partitioning and analyzing uniqueness properties of patterns.
Sudoku Squares and Chromatic Polynomials
TLDR
This Sudoku puzzle consists of a 9×9 grid in which some of the entries of the grid have a number from 1 to 9 and one is required to complete the grid in such a way that every row, every column, and every one of the nine 3× 3 sub-grids contain the digits from1 to 9 exactly once.
The science behind Sudoku.
TLDR
The article focuses on mathematical problems inherent in solving Sudoku puzzles and provides a mathematical analysis of how the puzzles are put together and solved.
Reducibility Among Combinatorial Problems
  • R. Karp
  • Computer Science
    50 Years of Integer Programming
  • 1972
TLDR
Throughout the 1960s I worked on combinatorial optimization problems including logic circuit design with Paul Roth and assembly line balancing and the traveling salesman problem with Mike Held, which made me aware of the importance of distinction between polynomial-time and superpolynomial-time solvability.
A New Algorithm for the Hypergraph Transversal Problem
TLDR
A new decomposition technique is given for solving the problem of finding all minimal transversals of a hypergraph, given by an explicit list of its hyperedges, with the following advantages: global parallelism, and new results on the complexity of generating minimalTransversals for new classes of hypergraphs, namely hyper graphs of bounded dual-conformality, andhypergraphs in which every edge intersects every minimaltransversal in a bounded number of vertices.
The size of the smallest uniquely completable set in order 8 Latin squares
In 1990, Kolesova, Lam and Thiel determined the 283,657 main classes of Latin squares of order 8. Using techniques to determine relevant Latin trades and integer programming, we examine
...
...