Sinkhorn solves Sudoku

Authors:
Todd K. Moon;Jacob H. Gunther;Joseph J. Kupin
Affiliations:
Electrical and Computer Engineering Department, Utah State University, Logan, UT;Electrical and Computer Engineering Department, Utah State University, Logan, UT;Center for Communications Research, Princeton, NJ
Venue:
IEEE Transactions on Information Theory
Year:
2009

Citing 2
Cited 2

Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)

Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
The capacity of low-density parity-check codes under message-passing decoding

IEEE Transactions on Information Theory

Solving single-digit sudoku subproblems

FUN'12 Proceedings of the 6th international conference on Fun with Algorithms
A hybrid AC3-tabu search algorithm for solving Sudoku puzzles

Expert Systems with Applications: An International Journal

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Abstract

The Sudoku puzzle is a discrete constraint satisfaction problem, as is the error correction decoding problem. We propose here an algorithm for solution to the Sinkhorn puzzle based on Sinkhorn balancing. Sinkhorn balancing is an algorithm for projecting a matrix onto the space of doubly stochastic matrices. The Sinkhorn balancing solver is capable of solving all but the most difficult puzzles. A proof of convergence is presented, with some information theoretic connections. A random generalization of the Sudoku puzzle is presented, for which the Sinkhorn-based solver is also very effective.