Support: UCARE grant awarded to Chris Reeson

1
Using Constraint Processing to Model, Solve
Support the Interactive Solving of Sudoku
Puzzles Christopher G. Reeson Berthe Y.
Choueiry Constraint Systems Laboratory
University of Nebraska-Lincoln Solver
sudoku.unl.edu/Solver Constructor
sudoku.unl.edu/Constructor
Goals
Constraint Propagation
Implementation
Solver is a Java applet that uses CP techniques
to support the user to play Sudoku. The player
can

• CP for Sudoku
• Study compare the effectiveness of constraint
  propagation algorithms
• CP for computer-human interaction
• Guide train human players
• Sudoku to illustrate teach CP
• Deconstructing Sudoku
• Demystify the puzzle
• Discourage students from losing time playing it

undo/redo any action
load an instance from the online library
assign all cells whose domains have a single
value
assign values to cells and play the game without
aid
FC
check the number of solutions left
Sudoku
AC
A Sudoku
display the remaining values in the domain of
each cell
apply a variety of CP techniques

• is well posed if it has a single solution
• is minimal if removing any given yields more
  than one solution
• is symmetric if the filled cells on the grid
  exhibit some axial symmetry

GAC
Solver detects errors and highlights the
variables in the broken constraint
Solver displays the number of hints. The user can
iterate through them. The user can choose the
type of hint the level of consistency
SAC
Hint highlights the cell to think about..
SGAC

• 2 types of hints Singleton Vital
• 8 levels FC, AC, Single GAC, GAC, Single SAC,
  SAC, Single SGAC, SGAC

15 on Royles web site1
CSP Model
Impact
Each cell is a variable whose domain is set of
numbers 19. The constraints are all-different
constraints on each row, column, and block.
Inspired a PhD student _at_ USC to use propagation
for constraint model generation from data
We can model each all-diff constraint as either a
set of binary mutex constraints...
or single non-binary alldiff constraints with
arity 9.
By Angelo Kai-Chen Huang _at_ USC

• Constructor
• Collaboration with an MS student _at_ USC
• Supports entering storing instances
• Counts displays all solutions
• Will support generalization to other Sudoku
  variations

• Conjectures
• SGAC ? relation (1,2)consistency
• SGAC can solve a well posed 9x9 Sudoku

Implementing both models allows the player to
compare and understand the effectiveness of
constraint propagation operating on each model.
References
Support UCARE grant awarded to Chris Reeson
CAREER Award 0133568 from the National Science
Foundation.

• Gordon Royle. Minimum Sudoku. people.csse.uwa.edu.
  au/gordon/sudokumin.php, 2005
• Helmut Simonis. Sudoku as a Constraint Problem.
  Workshop on Modeling and Refomulating CSPs, 2005