Abstract
We show that estimating the complexity (mean and distribution) of the instances of a fixed size Constraint Satisfaction Problem (CSP) can be very hard. We deal with the main two aspects of the problem: defining a measure of complexity and generating random unbiased instances. For the first problem, we rely on a general framework and a measure of complexity we presented at CISSE08. For the generation problem, we restrict our analysis to the Sudoku example and we provide a solution that also explains why it is so difficult.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E.P.K. Tsang, Foundations of Constraint Satisfaction, Academic Press, 1993.
H.W. Guesgen & J. Herztberg, A Perspective of Constraint-Based Reasoning, Lecture Notes in Artificial Intelligence, Springer, 1992.
D. Berthier: The Hidden Logic of Sudoku, Lulu.com, May 2007.
D. Berthier: The Hidden Logic of Sudoku (Second Edition), Lulu.com Publishers, December 2007.
D. Berthier: From Constraints to Resolution Rules; Part I: conceptual framework, CISSE08/SCSS, International Joint Conferences on Computer, Information, and System Sciences, and Engineering, December 4-12, 2009.
D. Berthier: From Constraints to Resolution Rules; Part II: chains, braids, confluence and T&E, CISSE08/SCSS, International Joint Conferences on Computer, Information, and System Sciences, and Engineering, December 4-12, 2009.
M. Gary & D. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, 1979.
G. Riley, CLIPS online documentation, http://clipsrules.sourceforge.net/OnlineDocs.html, 2008.
E.J. Friedmann-Hill, JESS Manual, http://www.jessrules.com/jess/docs/71, 2008.
G. Stertenbrink, suexg, http://www.setbb.com/phpb/viewtopic.php?t=206&mforum=sudoku, 2005.
B. Felgenhauer & F. Jarvis, Sudoku enumeration problems, http://www.afjarvis.staff.shef.ac.uk/sudoku/, 2006.
E. Russell & F. Jarvis, There are 5472730538 essentially different Sudoku grids, http://www.afjarvis.staff.shef.ac.uk/sudoku/sudgroup.html, 2006.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media B.V.
About this paper
Cite this paper
Berthier, D. (2010). Unbiased Statistics of a Constraint Satisfaction Problem – a Controlled-Bias Generator. In: Sobh, T., Elleithy, K. (eds) Innovations in Computing Sciences and Software Engineering. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9112-3_16
Download citation
DOI: https://doi.org/10.1007/978-90-481-9112-3_16
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-9111-6
Online ISBN: 978-90-481-9112-3
eBook Packages: Computer ScienceComputer Science (R0)