Generalized Arc Consistency Algorithms for Table Constraints: A Summary of Algorithmic Ideas

Yap, Roland H. C.; Xia, Wei; Wang, Ruiwei

doi:10.1609/aaai.v34i09.7086

Cited by 10 publications

(3 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(Dechter 1990) showed that the expressiveness of BCNs can be significantly improved with hidden variables. In addition, various binary encodings with hidden variables have been proposed to encode table constraints (Yap, Xia, and Wang 2020) as BCNs, such as the dual encoding (Dechter and Pearl 1989), hidden variable encoding (Rossi, Petrie, and Dhar 1990), double encoding (Stergiou and Walsh 1999) and bipartite encoding (Wang and Yap 2020). Although all constraint relations can be represented as table constraints, the tabulation of constraints may cause exponential blowup.…”

Section: Introductionmentioning

confidence: 99%

Encoding Constraints as Binary Constraint Networks Satisfying BTP

Wang

2024

AAAI

View full text Add to dashboard Cite

Recently, the Binary Constraint Tree (BCT), a tree structured Binary Constraint Network (BCN), has been shown to be more succinct than various ad-hoc constraints. In this paper, we investigate the modelling power of a well-known tractable hybrid class generalizing BCT, i.e. the class of BCNs satisfying Broken Triangle Property (BTP) called BTP Networks (BTPNs). We show that the consistency checker of BTPN can be computed by polysize monotone circuit, thus, some global constraints cannot be encoded as polysize BTPN, such as the AllDifferent and Linear constraints. Then our study reveals that BTPN is strictly more succinct than the DNNF constraint and all 14 ad-hoc constraints discussed in (Wang and Yap 2023), such as the context-free grammar, BCT and smart table constraints. Furthermore, we also show that BTPN is as powerful as DNNF in terms of computing various operations and queries. In addition, we prove that it is NP-hard to determine the minimum sized BTPN encoding a constraint.

show abstract

Section: Introductionmentioning

confidence: 99%

Encoding Constraints as Binary Constraint Networks Satisfying BTP

Wang

2024

AAAI

View full text Add to dashboard Cite

show abstract

“…Many algorithms (Yap, Xia, and Wang 2020) have been proposed to efficiently enforce Generalized Arc Consistency (GAC) on ad-hoc constraints. However, there is less work studying the constraint expressive power that can be useful for modelling CSPs, such as the constraint succinctness and the cost of operations/queries on constraints.…”

Section: Introductionmentioning

confidence: 99%

The Expressive Power of Ad-Hoc Constraints for Modelling CSPs

Wang

Yap

2023

AAAI

View full text Add to dashboard Cite

Ad-hoc constraints (also called generic constraints) are important for modelling Constraint Satisfaction Problems (CSPs). Many representations have been proposed to define ad-hoc constraints, such as tables, decision diagrams, binary constraint trees, automata and context-free grammars. However, prior works mainly focus on efficient Generalized Arc Consistency (GAC) propagators of ad-hoc constraints using the representations. In this paper, we ask a more fundamental question which bears on modelling constraints in a CSP as ad-hoc constraints, how the choice of constraints and operations affect tractability. Rather than ad-hoc constraints and their GAC propagators, our focus is on their expressive power in terms of succinctness (polysize) and cost of operations/queries (polytime). We use a large set of constraint families to investigate the expressive power of 14 existing ad-hoc constraints. We show a complete map of the succinctness of the ad-hoc constraints. We also present results on the tractability of applying various operations and queries on the ad-hoc constraints. Finally, we give case studies illustrating how our results can be useful for questions in the modelling of CSPs.

show abstract

“…Some ad-hoc constraints have been widely studied. For example, many Generalized Arc Consistency (GAC) algorithms have been proposed as the propagation algorithm to handle MDD constraints and (non-binary) table constraints (Yap, Xia, and Wang 2020). In this paper, we present a new representation for MDDs, showing how to transform any MDD constraint into Binary Constraint Trees (BCTs) and design MDD GAC propagators using BCTs.…”

Section: Introductionmentioning

confidence: 99%

Encoding Multi-Valued Decision Diagram Constraints as Binary Constraint Trees

Wang¹,

Yap²

2022

AAAI

Self Cite

View full text Add to dashboard Cite

Ordered Multi-valued Decision Diagram (MDD) is a compact representation used to model various constraints, such as regular constraints and table constraints. It can be particularly useful for representing ad-hoc problem specific constraints. Many algorithms have been proposed to enforce Generalized Arc Consistency (GAC) on MDD constraints. In this paper, we introduce a new compact representation called Binary Constraint Tree (BCT). We propose tree binary encodings to transform any MDD constraint into a BCT constraint. We also present a specialized algorithm enforcing GAC on the BCT constraint resulting from a MDD constraint. Experimental results on a large set of benchmarks show that the BCT GAC algorithm can significantly outperform state-of-the-art MDD as well as table GAC algorithms.

show abstract

Generalized Arc Consistency Algorithms for Table Constraints: A Summary of Algorithmic Ideas

Cited by 10 publications

References 34 publications

Encoding Constraints as Binary Constraint Networks Satisfying BTP

Encoding Constraints as Binary Constraint Networks Satisfying BTP

The Expressive Power of Ad-Hoc Constraints for Modelling CSPs

Encoding Multi-Valued Decision Diagram Constraints as Binary Constraint Trees

Contact Info

Product

Resources

About