A study of encodings of constraint satisfaction problems with 0/1 variables

Prosser, P. and Selensky, E. (2003) A study of encodings of constraint satisfaction problems with 0/1 variables. Lecture Notes in Computer Science, 2627, pp. 337-381.

Abstract

Many constraint satisfaction problems (csp's) are formulated with 0/1 variables. Sometimes this is a natural encoding, sometimes it is as a result of a reformulation of the problem, other times 0/1 variables make up only a part of the problem. Frequently we have constraints that restrict the sum of the values of variables. This can be encoded as a simple summation of the variables. However, since variables can only take 0/1 values we can also use an occurrence constraint, e.g. the number of occurrences of 1 must be k. Would this make a difference? Similarly, problems may use channelling constraints and encode these as a biconditional such as P « Q (i.e. P if and only if Q). This can also be encoded in a number of ways. Might this make a difference as well? We attempt to answer these questions, using a variety of problems and two constraint programming toolkits. We show that even minor changes to the formulation of a constraint can have a profound effect on the run time of a constraint program and that these effects are not consistent across constraint programming toolkits. This leads us to a cautionary note for constraint programmers: take note of how you encode constraints, and don't assume computational behaviour is toolkit independent.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Prosser, Dr Patrick
• Authors: Prosser, P., and Selensky, E.
• Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
• College/School: College of Science and Engineering > School of Computing Science
• Journal Name: Lecture Notes in Computer Science
• Publisher: Springer
• ISSN: 0302-9743
• Copyright Holders: Copyright © Springer 2003
• First Published: First published in Lecture Notes in Computer Science 2627:337-381
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher