Broken triangles: From value merging to a tractable class of general-arity constraint satisfaction problems

Cooper, Martin; Duchein, Aymeric; Mouelhi, Achref El; Escamocher, Guillaume; Terrioux, Cyril; Zanuttini, Bruno

doi:10.1016/j.artint.2016.02.001

Cited by 14 publications

(39 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In fact we will show that a more general class of problems, introduced by Cooper et al [17] and known as DGABTP, is decided by GAC. Cooper et al [17] showed that this class of problems has a polynomial-time solution algorithm based on variable elimination. Using Theorem 3 it is relatively simple to show that this class is also decided by GAC.…”

Section: Proposition 1 Any Instance I Whose Constraint Relations Are mentioning

confidence: 99%

“…These are the instances satisfying the so-called broken-triangle property. CSP instances satisfying the BTP (or its various extensions [17]) are the only known examples of classes of instances decided by GAC which are not closed under the action of removing a constraint, as the next example illustrates. {(2, 0), (2, 1), (2, 2), (1, 2)}.…”

Section: Hybrid Restrictionsmentioning

confidence: 99%

“…We begin with the definition of this non-binary class and state some of its properties which were established in [17].…”

Section: The Tractable Class Dgabtp Is Decided By Gacmentioning

confidence: 99%

“…Another application area is to identify sub-problems of a given problem that can be solved efficiently, that can be used as targets for problem reduction or pre-processing strategies [17]. We believe that the systematic identification of the properties needed for GAC decidability that we give here will lead to novel problem reduction and simplification strategies.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The power of propagation: when GAC is enough

Cohen

Jeavons

2016

Constraints

View full text Add to dashboard Cite

Considerable effort in constraint programming has focused on the development of efficient propagators for individual constraints. In this paper, we consider the combined power of such propagators when applied to collections of more than one constraint. In particular we identify classes of constraint problems where such propagators can decide the existence of a solution on their own, without the need for any additional search. Sporadic examples of such classes have previously been identified, including classes based on restricting the structure of the problem, restricting the constraint types, and some hybrid examples. However, there has previously been no unifying approach which characterises all of these classes: structural, language-based and hybrid. In this paper we develop such a unifying approach and embed all the known classes into a common framework. We then use this framework to identify a further class of problems that can be solved by propagation alone.

show abstract

Section: Proposition 1 Any Instance I Whose Constraint Relations Are mentioning

confidence: 99%

Section: Hybrid Restrictionsmentioning

confidence: 99%

“…We begin with the definition of this non-binary class and state some of its properties which were established in [17].…”

Section: The Tractable Class Dgabtp Is Decided By Gacmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The power of propagation: when GAC is enough

Cohen

Jeavons

2016

Constraints

View full text Add to dashboard Cite

show abstract

“…For the path concerned (denoted as p), D is defined on the basis of the acceptable ranges of the variables. One solution to the problem is a set of values to instantiate each variable within its domain, denoted as {<x 1 , V 1 >,<x 2 , V 2 >,…,<x i , V i >,<x i+1 , V i+1 >,…,<x n , V n >}(V i ∈D i ) to make p feasible, which means that each constraint in R should be satisfied [4].…”

Section: Introductionmentioning

confidence: 99%

A hybrid backtracking algorithm for automatic test data generation

et al. 2017

View full text Add to dashboard Cite

Original scientific paper As a fundamental issue in software testing, automatic test data generation is of crucial importance, which is essentially a constraint satisfaction problem and solved by search algorithms. In our previous research, branch and bound was proposed as our constraint solver and the look-ahead methods were elaborated. Based on interval arithmetic and symbolic execution, this paper focuses on the look-back or backtracking method, which is the hybridization of forward checking and conflict-directed backjumping, with the aim of improving the efficiency of backtracking in the search procedure. The closures of variables are used to facilitate the localization of the conflicts which cause dead ends. Empirical experiments prove the effectiveness of the proposed hybrid backtracking method and its applicability in engineering. Keywords: automatic test data generation; backtracking; closure; conflict-directed backjumping; forward checking Hibridni unatražni algoritam za automatsko generiranje podataka za ispitivanjeIzvorni znanstveni članak Kao osnovno pitanje u ispitivanju softvera, automatsko generiranje podataka za ispitivanje je od najveće važnosti, što je u biti problem zadovoljavanja ograničenja, a rješava se algoritmima pretraživanja. U našem prethodnom istraživanju za rješenje ograničenja predložena je metoda grananja i ograničavanja, a elaborirane su unaprijedne metode. Zasnovan na intervalnom aritmetičkom i simboličkom izvršenju, ovaj je rad usredotočen na unatražnu metodu, a to je povezivanje unaprijednog provjeravanja i unatražnog ispitivanja usmjerenog konflikta, u cilju poboljšanja učinkovitosti unatražnog praćenja u postupku traženja. Zatvaranja varijabli se koriste kako bi se olakšalo lociranje nesuglasica koje dovode do neriješenih rezultata (dead ends). Empirijski eksperimenti dokazuju učinkovitost predložene hibridne unatražne metode i njenu primjenljivost u inženjerstvu.Ključne riječi: automatsko generiranje podataka za ispitivanje; unaprijedno provjeravanje; unatražno praćenje; unatražno skakanje na osnovu konflikta; zatvaranje

show abstract

A Join-Based Hybrid Parameter for Constraint Satisfaction

Ganian

Ordyniak

Szeider

2019

Lecture Notes in Computer Science

View full text Add to dashboard Cite

We propose joinwidth, a new complexity parameter for the Constraint Satisfaction Problem (CSP). The definition of joinwidth is based on the arrangement of basic operations on relations (joins, projections, and pruning), which inherently reflects the steps required to solve the instance. We use joinwidth to obtain polynomial-time algorithms (if a corresponding decomposition is provided in the input) as well as fixed-parameter algorithms (if no such decomposition is provided) for solving the CSP. Joinwidth is a hybrid parameter, as it takes both the graphical structure as well as the constraint relations that appear in the instance into account. It has, therefore, the potential to capture larger classes of tractable instances than purely structural parameters like hypertree width and the more general fractional hypertree width (fhtw). Indeed, we show that any class of instances of bounded fhtw also has bounded joinwidth, and that there exist classes of instances of bounded joinwidth and unbounded fhtw, so bounded joinwidth properly generalizes bounded fhtw. We further show that bounded joinwidth also properly generalizes several other known hybrid restrictions, such as fhtw with degree constraints and functional dependencies. In this sense, bounded joinwidth can be seen as a unifying principle that explains the tractability of several seemingly unrelated classes of CSP instances.⋆ Robert Ganian acknowledges support by the Austrian Science Fund (FWF, Project P31336) and is also affiliated with FI MUNI, Czech Republic.

show abstract

Broken triangles: From value merging to a tractable class of general-arity constraint satisfaction problems

Cited by 14 publications

References 12 publications

The power of propagation: when GAC is enough

The power of propagation: when GAC is enough

A hybrid backtracking algorithm for automatic test data generation

A Join-Based Hybrid Parameter for Constraint Satisfaction

Contact Info

Product

Resources

About