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Universal Structures and the Logic of Forbidden Patterns [chapter]

Florent Madelaine
2006 Lecture Notes in Computer Science  
This contrasts with the case of unrestricted input structures, for which it is known that there are forbidden patterns problems that are not constraint satisfaction problems.  ...  We show that if the input comes from a class of connected structures with low tree-depth decomposition then every forbidden patterns problem is in fact a constraint satisfaction problem.  ...  The author is thankful to the first anonymous referee for advice on how to improve the exposition of this paper, and to the second referee for pointing out the implications of the independent work carried  ... 
doi:10.1007/11874683_31 fatcat:v3iuqwkbnrdwrp6lfly3jackyu

Universal Structures and the logic of Forbidden Patterns

Florent Madelaine, R. Ramanujam
2009 Logical Methods in Computer Science  
Forbidden Patterns Problems (FPPs) are a proper generalisation of Constraint Satisfaction Problems (CSPs).  ...  Note that our result holds in the general setting of problems over arbitrary relational structures (not just for graphs).  ...  The author is thankful to the first anonymous referee for advice on how to improve the exposition of this paper, and to the second referee for pointing out the implications of the independent work carried  ... 
doi:10.2168/lmcs-5(2:13)2009 fatcat:oe25lkzruzbdnasr7ac2jktgkm

Locally Consistent Constraint Satisfaction Problems with Binary Constraints [chapter]

Manuel Bodirsky, Daniel Král'
2005 Lecture Notes in Computer Science  
We determine ρ k (H) for all digraphs H that are not acyclic and show that lim k→∞ ρ k (H) = 1 if and only if H has tree duality.  ...  In addition, for graphs H with tree duality, we design an algorithm that computes in linear time for a given input graph G either a homomorphism from almost the entire graph G to H, or a subgraph of G  ...  Acknowledgement The authors are indebted to Zdeněk Dvořák for discussions on relative density of graphs and to Pavol Hell for his comments on tree duality.  ... 
doi:10.1007/11604686_26 fatcat:mcf2plq4k5gaxlvzfihj5zkftq

The Computational Structure of Monotone Monadic SNP and Constraint Satisfaction: A Study through Datalog and Group Theory

Tomás Feder, Moshe Y. Vardi
1998 SIAM journal on computing (Print)  
We divide CSP into subclasses and try to unify the collection of all known polytime algorithms for CSP problems and extract properties that make CSP problems NP-hard.  ...  Christos Papadimitriou suggested the connection between constraint satisfaction and two problems with a fixed structure that were previously studied, graph homomorphism and the boolean domain case.  ...  Theorem 19 A constraint-satisfaction problem has tree duality if and only if it has width 1. Proof.  ... 
doi:10.1137/s0097539794266766 fatcat:37znhdmmlvcdbfh3v4owh22baq

Optimal power flow over tree networks

Subhonmesh Bose, Dennice F. Gayme, Steven Low, K. Mani Chandy
2011 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton)  
In this paper we simplify this sufficient condition through a reformulation of the problem and prove that the condition is always satisfied for a tree network provided we allow over-satisfaction of load  ...  Recently, a sufficient condition has been found under which OPF has zero duality gap, which means that its solution can be computed efficiently by solving the convex dual problem.  ...  For future work, we will investigate the conditions for zero duality gap without the load over-satisfaction assumptions and study the effectiveness of the proposed algorithm using practical distribution  ... 
doi:10.1109/allerton.2011.6120323 dblp:conf/allerton/BoseGLC11 fatcat:dl5dx6eabza7jhkf6ikem3jhya

On the intersection of AI and OR

2001 Knowledge engineering review (Print)  
Hooker et al. (2000) propose a framework for unifying OR-style optimisation and AI-style constraint-satisfaction methods.  ...  for constraint optimization.  ...  Hooker et al. (2000) propose a framework for unifying OR-style optimisation and AI-style constraint-satisfaction methods.  ... 
doi:10.1017/s0269888901000066 fatcat:yp6fyeaknzcmvbzjq4wsvn7bhy

Dualities for Constraint Satisfaction Problems [chapter]

Andrei A. Bulatov, Andrei Krokhin, Benoit Larose
2008 Lecture Notes in Computer Science  
In a nutshell, a duality for a constraint satisfaction problem equates the existence of one homomorphism to the non-existence of other homomorphisms.  ...  In this survey paper, we give an overview of logical, combinatorial, and algebraic aspects of the following forms of duality for constraint satisfaction problems: finite duality, bounded pathwidth duality  ...  Acknowledgements The authors would like to thank Catarina Carvalho, Víctor Dalmau, Pavol Hell, Jarik Nešetřil, Claude Tardif and Pascal Tesson for useful discussions and helpful comments.  ... 
doi:10.1007/978-3-540-92800-3_5 fatcat:7mdouounufcfrgomcwrjzce5vy

Page 8504 of Mathematical Reviews Vol. , Issue 2004k [page]

2004 Mathematical Reviews  
Tools for constructing polynomial time algorithms such as consistency, tree-duality, pair consistency, and majority functions are also examined.  ...  Hence they provide a model more powerful than graph colourings, yet more manageable than constraint satisfaction problems.  ... 

Robust Satisfiability for CSPs

Víctor Dalmau, Andrei Krokhin
2013 ACM Transactions on Computation Theory  
An algorithm for a constraint satisfaction problem is called robust if it outputs an assignment satisfying at least a (1−f (ϵ))-fraction of constraints for each (1−ϵ)-satisfiable instance (i.e. such that  ...  We establish an algebraic framework for analyzing constraint satisfaction problems admitting an efficient robust algorithm with functions f of a given growth rate.  ...  We shall say that a structure has tree duality if it has an obstruction set consisting of tree structures. See for examples of structures with tree duality. Let (A, Γ) be a structure.  ... 
doi:10.1145/2540090 fatcat:25oavt5iyrfebaf5iyngqzadxu

Page 8259 of Mathematical Reviews Vol. , Issue 98M [page]

1998 Mathematical Reviews  
This leads to polynomial- time algorithms for computing globally consistent labelings for a large class of constraint satisfaction problems with continuous variables.” 90C Mathematical programming 98m:  ...  Summary: “We consider constraint satisfaction problems with variables in continuous, numerical domains.  ... 

Consistencies for Ultra-Weak Solutions in Minimax Weighted CSPs Using the Duality Principle [chapter]

Arnaud Lallouet, Jimmy H. M. Lee, Terrence W. K. Mak
2012 Lecture Notes in Computer Science  
Minimax Weighted Constraint Satisfaction Problems (formerly called Quantified Weighted CSPs) are a framework for modeling soft constrained problems with adversarial conditions.  ...  In estimating upper bounds, we propose two approaches based on the Duality Principle: duality of quantifiers and duality of constraints.  ...  To avoid solving multiple sub-problems, Minimax Weighted Constraint Satisfaction Problems (MWCSPs) (previously called Quantified Weighted Constraint Satisfaction Problems) [16] are proposed to tackle  ... 
doi:10.1007/978-3-642-33558-7_29 fatcat:shazybmrwbcbnauebdz5ox4j7y

Caterpillar Duality for Constraint Satisfaction Problems

Catarina Carvalho, Víctor Dalmau, Andrei Krokhin
2008 Logic in Computer Science  
Please consult the full DRO policy for further details. Abstract The study of constraint satisfaction problems definable in various fragments of Datalog has recently gained considerable importance.  ...  We consider constraint satisfaction problems that are definable in the smallest natural recursive fragment of Datalog -monadic linear Datalog with at most one EDB per rule.  ...  A constraint satisfaction problem is represented by a set of variables, a domain of values for each variable, and a set of constraints between variables.  ... 
doi:10.1109/lics.2008.19 dblp:conf/lics/CarvalhoDK08 fatcat:dvm6o6tibveopgpwxna3323mlq

Page 7085 of Mathematical Reviews Vol. , Issue 99j [page]

1999 Mathematical Reviews  
99}:68129 for pure constraints into one for mixed constraints.  ...  Summary: “Constraint satisfaction problems are common in artifi- cial intelligence.  ... 

Partial Enumeration and Curvature Regularization

Carl Olsson, Johannes Ulen, Yuri Boykov, Vladimir Kolmogorov
2013 2013 IEEE International Conference on Computer Vision  
This partial enumeration technique reduces complex highorder energy formulations to pairwise Constraint Satisfaction Problems with unary costs (uCSP), which can be efficiently solved using standard methods  ...  We propose a general minimization approach for large graphs based on enumeration of labelings of certain small patches.  ...  Our approach reduces high-order discrete energy formulations to pair-wise Constraint Satisfaction Problem with unary costs (uCSP).  ... 
doi:10.1109/iccv.2013.365 dblp:conf/iccv/OlssonUBK13 fatcat:iyrvh6cecfg7fdv5tnu6vnck2u

Duality in Optimization and Constraint Satisfaction [chapter]

J. N. Hooker
2006 Lecture Notes in Computer Science  
Two Kinds of Duals Duality is perennial theme in optimization and constraint satisfaction.  ...  The constraint satisfaction literature discusses constraint duals as well as search methods that are closely related to duality.  ...  The difference between the optimal value of the primal and the optimal value of the dual is the duality gap. The constraint set C implies f(x) ≥ v when f(x) ≥ v for all x ∈ D satisfying C.  ... 
doi:10.1007/11757375_3 fatcat:ve3xmr3ibjf27iifhokmmpot6e
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