Corpus ID: 18760406

Solving Sudoku Using Probabilistic Graphical Models

@inproceedings{Khan2008SolvingSU,
  title={Solving Sudoku Using Probabilistic Graphical Models},
  author={Sheehan Khan and Shahab Jabbari and Shahin Jabbari and Majid Ghanbarinejad},
  year={2008}
}
Sudoku is a popular number puzzle. Here, we model the puzzle as a probabilistic graphical model and drive a modification to the well-known sum-product and max-product message passing to solve the puzzle. In addition, we propose a Sudoku solver utilizing a combination of message passing and Sinkhorn balancing and show that as Sudoku puzzles become larger, the impact of loopy propagation does not increase. 

Figures and Tables from this paper

Using Probabilistic Graphic Models to Solve NP-Complete Puzzle Problems
Using Probabilistic Graphical Models to Solve NP-complete Puzzle Problems Probabilistic Graphical Models (PGMs) are commonly used in machine learning to solve problems stemming from medicine,Expand
Application of Message Passing and Sinkhorn Balancing Algorithms for Probabilistic Graphical Models
TLDR
This project attempts to modify the sum-product message passing algorithm to solve Sudoku, and implements a solution using Sinkhorn balancing to overcome the impact of loopy propagation and compare its performance with the former. Expand
An evolutionary approach to sudoku puzzles with filtered mutations
TLDR
This paper proposes a GA with sophisticated genetic mutations that mitigate the worsening of fitness values in extremely difficult sudoku puzzles, in which only a few given numbers are provided. Expand
Finding solutions to sudoku puzzles using human intuitive heuristics
  • N. Pillay
  • Computer Science
  • South Afr. Comput. J.
  • 2012
TLDR
The performance of the approach presented was found to be comparable to other methods used to solve Sudoku problems and in a number of cases produced better results. Expand
Sudoku at the Intersection of Classical and Quantum Computing
Even when quantum computers are widely available, it is unlikely that we will simply use them to solve all our problems. Rather we would use each computer for the types of problems it is best suitedExpand
Rešavanje problema CSP tehnikama svodjenja na problem SAT
TLDR
The main aim of this thesis is to improve CSP solving techniques that are using reduction to SAT, and two new hybrid encodings of CSPs to SAT are presented and they combine good sides of the existingencodings. Expand
A hardware generator for factor graph applications
  • James Demma, P. Athanas
  • Computer Science
  • 2014 International Conference on ReConFigurable Computing and FPGAs (ReConFig14)
  • 2014
TLDR
A framework is presented for rapid prototyping of hardware implementations of FG-based applications, and the framework has been applied to construct a Sudoku solver. Expand
Recurrent Relational Networks for Complex Relational Reasoning
TLDR
R recurrent relational networks are introduced which increase the suite of solvable tasks to those that require an order of magnitude more steps of relational reasoning and are applied to the BaBi textual QA dataset solving 19/20 tasks. Expand
Recurrent Relational Networks
TLDR
The recurrent relational network is introduced, a general purpose module that operates on a graph representation of objects that can augment any neural network model with the capacity to do many-step relational reasoning. Expand
End-to-end information extraction from business documents
TLDR
A recurrent neural network model that can capture long range context and compare it to a baseline logistic regression model corresponding to the current CloudScan production system are described. Expand
...
1
2
...

References

SHOWING 1-10 OF 18 REFERENCES
Solving Sudoku Using Combined Message Passing Algorithms
In this paper we apply message-passing algorithms to solve Sudoku puzzles. We provide explicit expression for the sum-product algorithm and the max-product algorithm and analyze the differenceExpand
Multiple Constraint Satisfaction by Belief Propagation: An Example Using Sudoku
  • T. Moon, J. Gunther
  • Mathematics
  • 2006 IEEE Mountain Workshop on Adaptive and Learning Systems
  • 2006
The popular Sudoku puzzle bears structural resemblance to the problem of decoding linear error correction codes: solution is over a discrete set, and several constraints apply. We express theExpand
Passing Messages to Lonely Numbers
  • H. Bauke
  • Computer Science
  • Computing in Science & Engineering
  • 2008
TLDR
Sudoku, a popular number puzzle, is a simple optimization problem that message-passing algorithms can help solve and is an ideal vehicle to demonstrate these methods' strengths and limitations. Expand
Complexity and Completeness of Finding Another Solution and Its Application to Puzzles
  • T. Yato, Takahiro Seta
  • Computer Science, Mathematics
  • IEICE Trans. Fundam. Electron. Commun. Comput. Sci.
  • 2003
TLDR
This paper considers n-ASP, the problem to find another solution when n solutions are given, and considers ASP-completeness, the completeness with respect to the parsimonious reductions which allow polynomial-time transformation. Expand
Solving, rating and generating Sudoku puzzles with GA
TLDR
The results presented in this paper seem to support the conclusion that the objectives of this study are reasonably well met with genetic algorithm optimization. Expand
On the optimality of solutions of the max-product belief-propagation algorithm in arbitrary graphs
TLDR
It is shown that the assignment based on a fixed point of max-product is a "neighborhood maximum" of the posterior probabilities: the posterior probability of the max- product assignment is guaranteed to be greater than all other assignments in a particular large region around that assignment. Expand
Generating Satisfiable Problem Instances
TLDR
This paper proposes a generator that only outputs satisfiable problem instances and shows how one can finely control the hardness of the satisfiable instances by establishing a connection between problem hardness and a new kind of phase transition phenomenon in the space of problem instances. Expand
Iterative Decoding for Sudoku and Latin Square Codes
This paper presents a new class of q-ary erasure-correcting codes based on Latin and Sudoku squares of order q, and an iterative decoding algorithm similar to the one used for the Low Density ParityExpand
Building Industrial Applications with Constraint Programming
TLDR
An overview of real-life applications developed with constraint logic programming and the concepts of global constraints, meta-heuristics and constraint visualisation, which are central to large scale constraint solving are introduced. Expand
Graph Theory with Applications
TLDR
The burgeoning of Graph Theory was first aware when I studied the 1940 paper of Brooks, Smith, Stone and Tutte in the Duke Mathematical Journal, ostensibly on squared rectangles, all in the Quest of the Perfect Square. Expand
...
1
2
...