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Symmetry in Constraint Programming [chapter]

Ian P. Gent, Karen E. Petrie, Jean-François Puget
2006 Foundations of Artificial Intelligence  
A key problem in constraint programming has long been recognised: search can revisit equivalent states over and over again.  ...  Symmetry in constraints has always been important but in recent years has become a major research area in its own right.  ...  to symmetry breaking in constraint programming.  ... 
doi:10.1016/s1574-6526(06)80014-3 fatcat:gcyfnj67ifelvpyjwwpruvwgq4

Automatically Exploiting Symmetries in Constraint Programming [chapter]

Arathi Ramani, Igor L. Markov
2005 Lecture Notes in Computer Science  
Symmetries are detected in high-level constraints by solving the graph automorphism problem on parse trees. Symmetry-breaking predicates are added during compilation.  ...  Linearity is preserved by the use of pseudo-Boolean (PB) constraints in conjunction with a 0-1 ILP solver that extends common SAT-solving techniques.  ...  We have not yet studied other types of SBPs such as those in [14] . Symmetries in linear programming problems have also been discussed in [17] .  ... 
doi:10.1007/11402763_8 fatcat:vzwf76fwpnh65c7ha2fsebgd2u

Symmetry Breaking in Subgraph Pattern Matching [chapter]

Stphane Zampelli, Yves Deville, Pierre Dupont
Trends in Constraint Programming  
In this paper, we develop symmetry breaking techniques for subgraph matching in order to increase the number of tractable instances.  ...  We also show how conditional value symmetries can be automatically detected and handled in the search process.  ...  In constraint programming, several authors [Larrosa and Valiente, 2002; To appear in the Sixth International Workshop on Symmetry in Constraint Satisfaction Problems (SymCon'06), Nantes, France, September  ... 
doi:10.1002/9780470612309.ch10 fatcat:dmcjjao2ebcolapent64tbvdvm

Exploiting Single-Cycle Symmetries in Branch-and-Prune algorithms [chapter]

Vicente Ruiz de Angulo, Carme Torras
Principles and Practice of Constraint Programming – CP 2007  
As a first attempt to exploit symmetries in continuous constraint problems, we focus on permutations of the variables consisting of one single cycle.  ...  A key concept in this procedure are the classes of symmetric boxes formed by bisecting a n-dimensional cube at the same point in all dimensions at the same time.  ...  Symmetry in Continuous Constraints Problems Symmetry exploitation in discrete constraint problems has received a great deal of attention lately [6, 4, 5, 11] .  ... 
doi:10.1007/978-3-540-74970-7_65 dblp:conf/cp/AnguloT07 fatcat:urfho463inet3jiqlqqtug5wui

Integrating Symmetry, Dominance, and Bound-and-Bound in a Multiple Knapsack Solver [chapter]

Alex S. Fukunaga
Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems  
We show experimentally that our new MKP solver, which integrates symmetry techniques from constraint programming and bound-and-bound techniques from operations research, significantly outperforms previous  ...  In this paper, we propose path-symmetry and path-dominance, which are instances of the symmetry detection by dominance detection approach for pruning symmetric nodes in the MKP branch-and-bound search  ...  Conclusions This paper presented an algorithm for the multiple knapsack problem which integrates techniques from constraint programming (symmetry-based pruning), operations research (bound-and-bound, as  ... 
doi:10.1007/978-3-540-68155-7_9 dblp:conf/cpaior/Fukunaga08 fatcat:4rwz7efkoje53jy336te4umfba

An Attempt to Dynamically Break Symmetries in the Social Golfers Problem [chapter]

Francisco Azevedo
Lecture Notes in Computer Science  
However, such constraints are imposed statically in the global problem model and are unable to detect symmetries that still occur in sub-problems after a partial labelling.  ...  Therefore, ordering constraints have been proposed and incorporated in set solvers.  ...  Nevertheless, much symmetry is still possible and, therefore, ordering constraints have been proposed and incorporated in set solvers.  ... 
doi:10.1007/978-3-540-73817-6_2 dblp:conf/csclp/Azevedo06 fatcat:nh6b3xt67jdgbg5bz6yiyw6xoi

A Novel Approach For Detecting Symmetries in CSP Models [chapter]

Christopher Mears, Maria Garcia de la Banda, Mark Wallace, Bart Demoen
Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems  
the kind of symmetries that can be inferred from the global constraints present in the model.  ...  While several powerful methods exist for automatically detecting symmetries in instances of constraint satisfaction problems (CSPs), current methods for detecting symmetries in CSP models are limited to  ...  A solution is a complete assignment that satisfies every constraint in C. Example 1.  ... 
doi:10.1007/978-3-540-68155-7_14 dblp:conf/cpaior/MearsBWD08 fatcat:6u55lomdg5gljoewwvxa6crbxe

lmaxRPCls: An Algorithm Utilizing Light Symmetry for Approximating maxRPC in Constraint Programming

Zhiying Xu, Shihui Song, Zhanshan Li
2017 Proceedings of the 2017 2nd International Conference on Control, Automation and Artificial Intelligence (CAAI 2017)   unpublished
Constraint satisfaction problem (CSP) can be widely applied in many areas. This paper investigates the maximum restricted path consistency algorithm.  ...  Experimental results show that lmaxRPCls performs better in most benchmark instances and it can improve the performance by 65% in the best case.  ...  In this paper, we focus on binary CSPs, and a constraint can be expressed by ij { 1 c , 2 c , … , e c } is a set of e constraints.  ... 
doi:10.2991/caai-17.2017.87 fatcat:ywvi4uuse5bnhdma6syepxssxy

Symmetry Breaking for Answer Set Programming [article]

Christian Drescher
2010 arXiv   pre-print
Furthermore, we explore symmetry breaking for answer set programming in two domains: first, constraint answer set programming as a novel approach to represent and solve constraint satisfaction problems  ...  These ideas are formulated as preprocessing and implemented in a completely automated flow that first detects symmetries from a given answer set program, adds symmetry-breaking constraints, and can be  ...  The lex-leader symmetry-breaking constraint that breaks every symmetry in a logic program can now be constructed by conjoining all of its permutation constraints.  ... 
arXiv:1008.5033v1 fatcat:q4dunj4fgzd73lvjtl4u32jvfu

BreakID: Static Symmetry Breaking for ASP (System Description) [article]

Jo Devriendt, Bart Bogaerts
2016 arXiv   pre-print
In this paper, we port the state-of-the-art SAT symmetry breaker BreakID to answer set programming (ASP).  ...  The result is a lightweight tool that can be plugged in between the grounding and the solving phases that are common when modelling in ASP.  ...  In constraint programming, work has been done on composing the symmetry properties of global constraints into a symmetry group of the original problem [33] .  ... 
arXiv:1608.08447v1 fatcat:enkeaaj5brhljo3zauy6mdgzym

The Steel Mill Slab Design Problem Revisited [chapter]

Pascal Van Hentenryck, Laurent Michel
2008 Lecture Notes in Computer Science  
This paper shows that a simple search procedure breaking symmetries dynamically leads to a constraint program solving the problem in a few seconds, while maintaining the completeness of the approach and  ...  Contrary to earlier approaches, their model does not use 0/1 variables but exploits the traditional expressiveness of constraint programming.  ...  This paper shows that their constraint-programming model with a simple, dynamic symmetry-breaking scheme leads to a constraint program solving the problem in a few seconds, while maintaining the completeness  ... 
doi:10.1007/978-3-540-68155-7_41 fatcat:2yf4nqh2izcirbw3avtcvt76mu

Symmetry-breaking Answer Set Solving [article]

Christian Drescher and Oana Tifrea and Toby Walsh
2010 arXiv   pre-print
In the context of Answer Set Programming, this paper investigates symmetry-breaking to eliminate symmetric parts of the search space and, thereby, simplify the solution process.  ...  Symmetries are then broken by introducing symmetry-breaking constraints. For this purpose, we formulate a preprocessor that integrates a graph automorphism system.  ...  The lex-leader symmetry-breaking constraint that breaks every symmetry in a logic program can now be constructed by conjoining all of its permutation constraints. Example 6.  ... 
arXiv:1008.1809v1 fatcat:7f732eyxnfaadohihy53aojalu

Symmetry-breaking answer set solving

Christian Drescher, Oana Tifrea, Toby Walsh
2011 AI Communications  
Fig. 4 illustrates the gen- The lex-leader symmetry-breaking constraint that eral structure of a coloured graph construction of breaks every symmetry in a logic program can now  ...  The logic program is then A rule of form (1) can be seen as a constraint preprocessed by adding symmetry-breaking con- on the answer sets of a program, stating that straints  ... 
doi:10.3233/aic-2011-0495 fatcat:zyoxywaotvcrvdjqfcqk7r3jaq

Detecting Orbitopal Symmetries [chapter]

Timo Berthold, Marc E. Pfetsch
2009 Operations Research Proceedings 2008  
Orbitopes can be used to handle symmetries which arise in integer programming formulations with an inherent assignment structure.  ...  We investigate the detection of symmetries appearing in this approach.  ...  Symmetries in Binary Programs In this section, we introduce symmetries in binary programs and their detection by color-preserving graph automorphisms.  ... 
doi:10.1007/978-3-642-00142-0_70 fatcat:ocbwiegr5ff5fkdhegg3q7kbu4

Improved method of cell placement with symmetry constraints for analog IC layout design

Shinichi Kouda, Chikaaki Kodama, Kunihiro Fujiyoshi
2006 Proceedings of the 2006 international symposium on Physical design - ISPD '06  
Symmetric feasible seq-pair for each symmetry group.  ...  Placement is obtained from a given seq-pair and symmetry constraints by linear programming. Feature 2. Speed-up is done by reducing the number of variables and linear constraint expressions.  ...  Proposed method Linear programming Coordinate of left (lower) edge of each cell To obtain constraints expressions from sequence-pair -Coordinate of each cell with symmetry constraints is determined  ... 
doi:10.1145/1123008.1123050 dblp:conf/ispd/KoudaKF06 fatcat:fapoaewqgzgifcnytrbeqlqziu
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