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Binary Encodings of Non-binary Constraint Satisfaction Problems: Algorithms and Experimental Results

N. Samaras, K. Stergiou
2005 The Journal of Artificial Intelligence Research  
A non-binary Constraint Satisfaction Problem (CSP) can be solved directly using extended versions of binary techniques.  ...  Theoretical and empirical results show that, for certain classes of non-binary constraints, binary encodings are a competitive option, and in many cases, a better one than the non-binary representation  ...  We would also like to thank the anonymous reviewers of an earlier version of this paper for their very useful comments and suggestions.  ... 
doi:10.1613/jair.1776 fatcat:evl2bad6gbhyzpqvobj6mi7ftm

Local Search on SAT-encoded Colouring Problems [chapter]

Steven Prestwich
2004 Lecture Notes in Computer Science  
Constraint satisfaction problems can be SAT-encoded in more than one way, and the choice of encoding can be as important as the choice of search algorithm.  ...  Theoretical results are few but experimental comparisons have been made between encodings, using both local and backtrack search algorithms.  ...  Unfortunately there are several ways of SAT-encoding constraint satisfaction (CSP) and other problems, and few guidelines on how to choose among them.  ... 
doi:10.1007/978-3-540-24605-3_9 fatcat:2jxx4so7hbgp7omgvf545w44f4

Algorithms for Quantified Constraint Satisfaction Problems [chapter]

Nikos Mamoulis, Kostas Stergiou
2004 Lecture Notes in Computer Science  
Many propagation and search algorithms have been developed for constraint satisfaction problems (CSPs). In a standard CSP all variables are existentially quantified.  ...  Finally, we test experimentally the algorithms and methods proposed.  ...  Acknowledgements Kostas Stergiou is a member of the APES research group and would like to thank all other members. We especially thank I. Gent, P. Nightingale, and A. Rowley.  ... 
doi:10.1007/978-3-540-30201-8_60 fatcat:rq63rbq76nd47hlgtiy2q42l6y

The hardest random SAT problems [chapter]

Ian P. Gent, Toby Walsh
1994 Lecture Notes in Computer Science  
We also report results suggesting that better algorithms will be unable to eliminate this constraint gap and hence will continue to nd very di cult problems in this region.  ...  We describe a detailed experimental investigation of the phase transition for several di erent classes of satis ability problems including random k-SAT, the constant probability model, and encodings of  ...  of Computer Science at Cornell University, for their constructive comments and for rather a lot of CPU cycles.  ... 
doi:10.1007/3-540-58467-6_31 fatcat:vyuydcqzovhlveqdllsm3kh5qu

Solving the Car-Sequencing Problem as a Non-binary CSP [chapter]

Mihaela Butaru, Zineb Habbas
2005 Lecture Notes in Computer Science  
A search algorithm based on non-binary forward checking (nFC) is used to solve the car-sequencing problem.  ...  The choice of value ordering heuristics having a dramatic effect on solution time for this problem, different ordering heuristics were implementented.  ...  Experimental Results Implementation and Experimental Framework In our implementation, we generate the car-sequencing problem as a non-binary CSP with n variables (the slots in the sequence), d values  ... 
doi:10.1007/11564751_78 fatcat:v2s3d3boufeo5lmcadel2vqf64

MinSAT versus MaxSAT for Optimization Problems [chapter]

Josep Argelich, Chu-Min Li, Felip Manyà, Zhu Zhu
2013 Lecture Notes in Computer Science  
Despite their similarities, MaxSAT and MinSAT use different encodings and solving techniques to cope with optimization problems.  ...  In this paper we describe a new weighted partial MinSAT solver, define original MinSAT encodings for relevant combinatorial problems, propose a new testbed for evaluating MinSAT, report on an empirical  ...  Experimental results for random binary MaxCSP, graph coloring, and kbtree instances.  ... 
doi:10.1007/978-3-642-40627-0_13 fatcat:mshvhm2i5vdubb5ttsjtbowhva

Inverse Problems, Constraint Satisfaction, Reversible Logic, Invertible Logic and Grover Quantum Oracles for Practical Problems [chapter]

Marek Perkowski
2020 Lecture Notes in Computer Science  
In contrast, such methodologies have been already created for classical Constraint Satisfaction Problems.  ...  The goal of this invited talk is to show results of some initial research towards creating systematic methodologies to program quantum computers that solve search problems in Artificial Intelligence, Logic  ...  Introduction There are two important and large classes of problems: Constraint Satisfaction Problems (CSP) and optimization problems.  ... 
doi:10.1007/978-3-030-52482-1_1 fatcat:xw3kgmienzhh7mmfi4u3n6h7d4

Permutation Problems and Channelling Constraints [chapter]

Toby Walsh
2001 Lecture Notes in Computer Science  
These results will aid users of constraints to choose a model for a permutation problem, and a local consistency property to enforce upon it.  ...  We also compare the constraint tightness in SAT encodings of these permutation problems.  ...  He thanks the other members of the APES research group (, especially Barbara Smith for helpful discussions, and Carla Gomes and her colleagues for providing code to generate  ... 
doi:10.1007/3-540-45653-8_26 fatcat:iy64d2qn4zhw3iqxfdbkybygga

Solving quantified constraint satisfaction problems

Ian P. Gent, Peter Nightingale, Andrew Rowley, Kostas Stergiou
2008 Artificial Intelligence  
We make a number of contributions to the study of the Quantified Constraint Satisfaction Problem (QCSP).  ...  The QCSP is an extension of the constraint satisfaction problem that can be used to model combinatorial problems containing contingency or uncertainty.  ...  Acknowledgements We would like to thank the anonymous reviewers for their comments and suggestions that helped greatly improve the presentation of this paper.  ... 
doi:10.1016/j.artint.2007.11.003 fatcat:3fmxgpa6rrbojiueahzaual7b4

Solving Over-Constrained Problems with SAT Technology [chapter]

Josep Argelich, Felip Manyà
2005 Lecture Notes in Computer Science  
Finally, we present an experimental investigation to assess the performance of our approach on a representative sample of instances (random 2-SAT, Max-CSP, and graph coloring).  ...  We present a new generic problem solving approach for overconstrained problems based on Max-SAT.  ...  The first column shows the parameters given to the generator of random binary CSPs, and the remaining columns show the experimental results obtained.  ... 
doi:10.1007/11499107_1 fatcat:deqhgvnybfdj7jutifhwvrt4hy

Valued Workflow Satisfiability Problem [article]

Jason Crampton and Gregory Z. Gutin and Daniel Karapetyan
2015 arXiv   pre-print
In this paper, we consider the problem of finding the "least bad" assignment of users to workflow steps by assigning a weight to each policy and constraint violation.  ...  To this end, we introduce a framework for associating costs with the violation of workflow policies and constraints and define the valued workflow satisfiability problem (Valued WSP), whose solution is  ...  They encode the problem of minimizing this cost as a integer linear program-ming problem and use off-the-shelf software to solve the resulting problem.  ... 
arXiv:1501.07814v1 fatcat:245ejh23wfcdhgnxgetqafacpa

On Generators of Random Quasigroup Problems [chapter]

Roman Barták
2006 Lecture Notes in Computer Science  
Problems that can be sampled randomly are a good source of test suites for comparing quality of constraint satisfaction techniques.  ...  We also re-formulate the algorithm for generating QWH that is much faster than the original generator. Finally, we provide an experimental comparison of all presented generators.  ...  This makes the problem non-trivial and hence interesting as a benchmark for comparing constraint satisfaction techniques.  ... 
doi:10.1007/11754602_12 fatcat:sfjrqmtew5aevciwicx5hxkmqu

Exact Max-SAT solvers for over-constrained problems

Josep Argelich, Felip Manyà
2006 Journal of Heuristics  
Finally, we report an experimental investigation on a representative sample of instances (random 2-SAT, Max-CSP, graph coloring, pigeon hole and quasigroup completion) which provides experimental evidence  ...  Our solvers are branch and bound algorithms equipped with original lazy data structures, powerful inference techniques, good quality lower bounds, and original variable selection heuristics.  ...  We used SAT-encoded random binary CSPs and solved the Max-CSP problem. A constraint satisfaction problem (CSP) consists of a set of variables, each with a domain of values, and a set of constraints.  ... 
doi:10.1007/s10732-006-7234-9 fatcat:fso2fx27lrdvbgelglqxm5apkm

Generating highly balanced sudoku problems as hard problems

Carlos Ansótegui, Ramón Béjar, Cèsar Fernández, Carla Gomes, Carles Mateu
2010 Journal of Heuristics  
Ansótegui et al. niques for solving and modeling Sudoku problems, namely, Constraint Satisfaction Problem (CSP) and Satisfiability Problem (SAT) approaches.  ...  Experimentally, we show that the more balanced are the constraints, the higher the complexity of solving the GSP instances, and that GSP is harder than the Quasigroup Completion Problem (QCP), a problem  ...  Section 5 studies the worst-case complexity of Sudoku problems for the case of non-square region shape. Section 6 is devoted to encode the GSP to SAT and CSP problems.  ... 
doi:10.1007/s10732-010-9146-y fatcat:ldh3ldjcubaptkykurxevcz7lq

Mapping Problems with Finite-Domain Variables to Problems with Boolean Variables [chapter]

Carlos Ansótegui, Felip Manyà
2005 Lecture Notes in Computer Science  
Our results provide empirical evidence that encoding combinatorial problems with the mappings defined here can lead to substantial performance improvements in complete SAT solvers.  ...  We define a collection of mappings that transform many-valued clausal forms into satisfiability equivalent Boolean clausal forms, analyze their complexity and evaluate them empirically on a set of benchmarks  ...  problem (SAT) and then solving the resulting encodings with algorithms for SAT.  ... 
doi:10.1007/11527695_1 fatcat:ie5a3c34ybgg3mhmmxvfuycw7a
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