Automatically improving constraint models in Savile Row through associative-commutative common subexpression elimination

Peter Nightingale*, Ozgur Akgun, Ian P. Gent, Christopher Jefferson, Ian Miguel

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

20 Citations (Scopus)

Abstract

When solving a problem using constraint programming, constraint modelling is widely acknowledged as an important and difficult task. Even a constraint modelling expert may explore many models and spend considerable time modelling a single problem. Therefore any automated assistance in the area of constraint modelling is valuable. Common sub-expression elimination (CSE) is a type of constraint reformulation that has proved to be useful on a range of problems. In this paper we demonstrate the value of an extension of CSE called Associative-Commutative CSE (AC-CSE). This technique exploits the properties of associativity and commutativity of binary operators, for example in sum constraints. We present a new algorithm, X-CSE, that is able to choose from a larger palette of common subexpressions than previous approaches. We demonstrate substantial gains in performance using X-CSE. For example on BIBD we observed speed increases of more than 20 times compared to a standard model and that using X-CSE outperforms a sophisticated model from the literature. For Killer Sudoku we found that X-CSE can render some apparently difficult instances almost trivial to solve, and we observe speed increases up to 350 times. For BIBD and Killer Sudoku the common subexpressions are not present in the initial model: an important part of our methodology is reformulations at the preprocessing stage, to create the common subexpressions for X-CSE to exploit. In summary we show that X-CSE, combined with preprocessing and other reformulations, is a powerful technique for automated modelling of problems containing associative and commutative constraints.
Original languageEnglish
Title of host publicationPrinciples and Practice of Constraint Programming
Subtitle of host publication20th International Conference, CP 2014, Lyon, France, September 8-12, 2014. Proceedings
EditorsBarry O'Sullivan
Place of PublicationCham
PublisherSpringer
Pages590-605
Number of pages16
ISBN (Electronic)9783319104287
ISBN (Print)9783319104270
DOIs
Publication statusPublished - 8 Sept 2014
Event20th International Conference on the Principles and Practice of Constraint Programming (CP 2014) - Lyon, France
Duration: 8 Sept 201412 Sept 2014
Conference number: 20

Publication series

NameLecture Notes in Computer Science
PublisherSpringer International Publishing AG
Volume8656 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference20th International Conference on the Principles and Practice of Constraint Programming (CP 2014)
Abbreviated titleCP 2014
Country/TerritoryFrance
CityLyon
Period8/09/1412/09/14

Keywords

  • Symmetry
  • Breaking
  • System

Fingerprint

Dive into the research topics of 'Automatically improving constraint models in Savile Row through associative-commutative common subexpression elimination'. Together they form a unique fingerprint.

Cite this