A comparison of several enumerative algorithms for Sudoku

Sudoku is a puzzle played of an n × n grid where n is the square of a positive integer m. The most common size is n=9. The grid is partitioned into n subgrids of size m × m. The player must place exactly one number from the set N={1, ..., n} in each row and each column of as well as in each subgrid....

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:The Journal of the Operational Research Society Ročník 65; číslo 10; s. 1602 - 1610
Hlavní autoři: Coelho, Leandro C, Laporte, Gilbert
Médium: Journal Article
Jazyk:angličtina
Vydáno: London Taylor & Francis 01.10.2014
Palgrave Macmillan
Palgrave Macmillan UK
Taylor & Francis Ltd
Témata:
Algorithms
backtracking
Business and Management
constraint programming
Datasets
Game theory
General Paper
General Papers
Heuristics
Integer programming
Integers
linear and non-linear integer programming
Linear programming
Management
Mathematical analysis
Mathematical models
Mathematical programming
Mathematical puzzles
Modeling
Operations research
Operations Research/Decision Theory
puzzle
Puzzles
Studies
Sudoku
backtracking
linear and non-linear integer programming
Sudoku
puzzle
constraint programming
ISSN:0160-5682, 1476-9360
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí:Sudoku is a puzzle played of an n × n grid where n is the square of a positive integer m. The most common size is n=9. The grid is partitioned into n subgrids of size m × m. The player must place exactly one number from the set N={1, ..., n} in each row and each column of as well as in each subgrid. A grid is provided with some numbers already in place, called givens. In this paper, some relationships between Sudoku and several operations research problems are presented. We model the problem by means of two mathematical programming formulations. The first one consists of an integer linear programming model, while the second one is a tighter non-linear integer programming formulation. We then describe several enumerative algorithms to solve the puzzle and compare their relative efficiencies. Two basic backtracking algorithms are first described for the general Sudoku. We then solve both formulations by means of constraint programming. Computational experiments are performed to compare the efficiency and effectiveness of the proposed algorithms. Our implementation of a backtracking algorithm can solve most benchmark instances of size 9 within 0.02 s, while no such instance was solved within that time by any other method. Our implementation is also much faster than an existing alternative algorithm.
Bibliografie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0160-5682
1476-9360
DOI:10.1057/jors.2013.114