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CSPs with Global Modular Constraints: Algorithms and Hardness via Polynomial Representations
[article]
2019
arXiv
pre-print
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The inspiration for our study comes from a recent work by N\"agele, Sudakov, and Zenklusen on submodular minimization with a global congruence constraint. ...
In both cases, the analysis of our algorithm as well as the hardness reduction rely on these polynomial representations, highlighting an interesting algebraic common ground between hard cases for our algorithms ...
The main focus of this work is to investigate CSPs with a much less strict global constraint, which we refer to as a modular (or congruency) constraint. ...
arXiv:1902.04740v1
fatcat:xv7eh5ybgjezfiimqsdmpr2g4q
Transformations of representation in constraint satisfaction
2015
Constraints
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I also develop finer grained techniques, by allowing vertices of the microstructure representation to be assigned colours, and the variables to be ordered. ...
The main technique I use is a transformation of a CSP instance to the microstructure representation. ...
If the arity of constraints in a CSP is bounded, then the complete representation has size at most polynomial in the size of the usual representations, and provides a useful and regular representation ...
doi:10.1007/s10601-015-9224-8
fatcat:lollakqzx5h7xeajtfrmaz6u4q
Constraint Logic Programming
[chapter]
2003
Constraint Processing
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Constraint Logic Programming (CLP) is one of the most successful branches of Logic Programming; it attracts the interest of theoreticians and practitioners, and it is currently used in many commercial ...
Current CLP engines include technologies and results developed in other communities, which themselves discovered logic as an invaluable tool to model and solve real-life problems. ...
This research has been partially funded by PRIN 2008 project 'Innovative and multi-disciplinary approaches for constraint and preference reasoning'. ...
doi:10.1016/b978-155860890-0/50016-5
fatcat:mxvb5ji2sjelnb3rn2sxrhq5lm
Constraint Logic Programming
[chapter]
2010
Lecture Notes in Computer Science
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Constraint Logic Programming (CLP) is one of the most successful branches of Logic Programming; it attracts the interest of theoreticians and practitioners, and it is currently used in many commercial ...
Current CLP engines include technologies and results developed in other communities, which themselves discovered logic as an invaluable tool to model and solve real-life problems. ...
This research has been partially funded by PRIN 2008 project 'Innovative and multi-disciplinary approaches for constraint and preference reasoning'. ...
doi:10.1007/978-3-642-14309-0_4
fatcat:ozoif5tgorhw3mbhnyw3aijpfu
Quantum-accelerated constraint programming
2021
Quantum
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Leveraging existing quantum algorithms, we introduce a quantum-accelerated filtering algorithm for the alldifferent global constraint and discuss its applicability to a broader family of global constraints ...
In CP, problems are modeled with constraints that describe acceptable solutions and solved with backtracking tree search augmented with logical inference. ...
We identify a broader family of global constraints, including the global cardinality constraint (gcc) and the inverse constraint, whose domain consistency filtering algorithms can be accelerated with quantum ...
doi:10.22331/q-2021-09-28-550
fatcat:delihkthejbpfb7iwybs7z7yh4
Quantum-accelerated constraint programming
[article]
2021
arXiv
pre-print
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Leveraging existing quantum algorithms, we introduce a quantum-accelerated filtering algorithm for the global constraint and discuss its applicability to a broader family of global constraints with similar ...
In CP, problems are modeled with constraints that describe acceptable solutions and solved with backtracking tree search augmented with logical inference. ...
We identify a broader family of global constraints, including the global cardinality constraint (gcc) and the inverse constraint, whose domain consistency filtering algorithms can be accelerated with quantum ...
arXiv:2103.04502v2
fatcat:g2a6fu2tt5cdvgvziwdy5tgtla
A Survey on String Constraint Solving
[article]
2021
arXiv
pre-print
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2020 pre-print arXiv:2002.02376v6 fatcat:nbqihxzv2rekxe4rkzruuw6kwaOther Versions
String constraint solving refers to solving combinatorial problems involving constraints over string variables. ...
String solving approaches have become popular over the last years given the massive use of strings in different application domains like formal analysis, automated testing, database query processing, and ...
polynomial time. ...
arXiv:2002.02376v8
fatcat:why6oeufmrbozbl22jlf7yivea
When symmetries are not enough: a hierarchy of hard Constraint Satisfaction Problems
[article]
2021
arXiv
pre-print
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We show that the encoded structures retain desirable algebraic properties of the original structures, but that the constraint satisfaction problems (CSPs) associated with these structures can be badly ...
Finally, we obtain a concrete algebraic criterion which could constitute a description of the delineation between tractability and NP-hardness in the dichotomy conjecture for first-order reducts of finitely ...
Figure 1 . 1 A vague representation of the hierarchy algorithm witnessing said tractability. The connection with questions
Figure 3 . 3 Sources and destinations of operators. ...
arXiv:2002.07054v2
fatcat:7gjieagt2rdthb7imxs535e3a4
Weight constraint programs with evaluable functions
2010
Annals of Mathematics and Artificial Intelligence
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A main advantage of this approach is that global constraints implemented in such CSP solvers become available to ASP. ...
Computationally, we provide a translation from loop completions of these programs to instances of the Constraint Satisfaction Problem (CSP) and use the off-the-shelf CSP solvers to compute the answer sets ...
This is an advantage compared with ASP encodings and solvers without global constraints. ...
doi:10.1007/s10472-011-9237-y
fatcat:bza5wvp2sbgfxn3i7vxxjdsjkm
Enhancing set constraint solvers with lexicographic bounds
2007
Journal of Heuristics
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In this paper we present and evaluate a new means towards improving the practical reasoning power of Finite Set (FS) constraint solvers to better address such set problems with a particular attention to ...
, and allow for active symmetry breaking using ordering constraints. ...
need to identify and create specialized global constraint propagation algorithms. ...
doi:10.1007/s10732-007-9028-0
fatcat:4aih7z5wtvdgnoa2a3ngqtb7w4
Deductive temporal reasoning with constraints
2013
Journal of Applied Logic
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In this paper we consider a logic which is a combination of standard propositional linear time temporal logic with cardinality constraints restricting the numbers of literals that can be satisfied at any ...
We propose a tableau-like algorithm for checking the satisfiability of formulae in this logic, provide details of a prototype implementation and present experimental results using the prover. ...
Acknowledgements The authors were partially supported by EPSRC grants GR/S63182 (Dixon, Konev) and EP/D052548 (Fisher). ...
doi:10.1016/j.jal.2012.07.001
fatcat:m7lrdxd5lnfyxkyqyh7nylprpq
Unicast and Multicast Qos Routing with Soft Constraint Logic Programming
[article]
2008
arXiv
pre-print
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We present a formal model to represent and solve the unicast/multicast routing problem in networks with Quality of Service (QoS) requirements. ...
and solving the constraints imposed on them (e.g. delay < 40msec), thus finding a solution to QoS routing problems. ...
a cost, level of preference, . . . ), and constraints are combined via the × operation and compared via the ≤ S ordering. ...
arXiv:0704.1783v3
fatcat:aqsrqz3bzzdyhdyf3e3mv7qg5i
Interval propagation to reason about sets: Definition and implementation of a practical language
1997
Constraints
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In addition, Conjunto provides us with a set of constraints called graduated constraints (e.g. the set cardinality) which map sets onto arithmetic terms. ...
This makes di cult a natural and concise modelling as well as an e cient solving of a class of N P -complete combinatorial search problems dealing with sets. ...
GERVET inary versions of the thesis and to Mark Wallace for his valuable comments and corrections which s u b s t a n tially improved my w ork. ...
doi:10.1007/bf00137870
fatcat:vqzf2j7l7bc6tl4yhpkko6vwam
Commutative idempotent groupoids and the constraint satisfaction problem
2015
Algebra Universalis
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The idea of global tractability, that a single algorithm exists which solves CSP(∆) for every finite subset ∆, is clearly at least as strong as local tractability. ...
Since SL ⊆ T 1 ⊆ T 2 , these varieties are not congruence modular (and hence cannot be shown tractable via the result of [18] ). ...
doi:10.1007/s00012-015-0323-6
fatcat:acdbzdlolfd6zoouqlg2ji67xi
CNF Satisfiability in a Subspace and Related Problems
[article]
2021
arXiv
pre-print
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Clearly, it is no easier than k-SAT, and might be harder. Indeed, via simple reductions we show NP-hardness for k=2 and W[1]-hardness parameterized by the co-dimension of the subspace. ...
We give a simple branching algorithm with runtime 1.5^r for 2-SUB-SAT, where r is the subspace dimension and an O^*(1.4312)^n time algorithm where n is the number of variables. ...
Acknowledgment We thank anonymous reviewers for useful comments and pointers to the literature. ...
arXiv:2108.05914v1
fatcat:btn7airnijg47h5xkaiplandoa
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