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Approximation for Maximum Surjective Constraint Satisfaction Problems [article]

Walter Bach, Hang Zhou
2011 arXiv   pre-print
Maximum surjective constraint satisfaction problems (Max-Sur-CSPs) are computational problems where we are given a set of variables denoting values from a finite domain B and a set of constraints on the  ...  We study the approximation performance that can be acccchieved by algorithms for these problems, mainly by investigating their relation with Max-CSPs (which are the corresponding problems without the surjectivity  ...  The maximum surjective constraint satisfaction problem Max-Sur-CSP(B) is defined similarly, only we insist that the function h be surjective.  ... 
arXiv:1110.2953v1 fatcat:gdfk7mfaengyjnscr4ljrau5b4

Approximability of the Maximum Solution Problem for Certain Families of Algebras [chapter]

Peter Jonsson, Johan Thapper
2009 Lecture Notes in Computer Science  
We study the approximability of the maximum solution problem.  ...  This problem is an optimisation variant of the constraint satisfaction problem and it captures a wide range of interesting problems in, for example, integer programming, equation solving, and graph theory  ...  The constraint satisfaction problem over the constraint language Γ , denoted CSP(Γ ), is the decision problem with instance (V, A, C).  ... 
doi:10.1007/978-3-642-03351-3_21 fatcat:iyoy6rxvufarxajkb2zx626uoq

The complexity of Boolean surjective general-valued CSPs [article]

Peter Fulla, Hannes Uppman, Stanislav Zivny
2017 arXiv   pre-print
For the maximisation problem of Q_≥ 0-valued surjective VCSPs, we also establish a dichotomy theorem with respect to approximability.  ...  Valued constraint satisfaction problems (VCSPs) are discrete optimisation problems with a (Q∪{∞})-valued objective function given as a sum of fixed-arity functions.  ...  This fundamental problem is an example of a Boolean valued constraint satisfaction problem (VCSP). Let D be an arbitrary finite set called the domain.  ... 
arXiv:1702.04679v4 fatcat:szikvlidxfbudjr24nawo4yk4a

On the subgraph epimorphism problem

Steven Gay, François Fages, Thierry Martinez, Sylvain Soliman, Christine Solnon
2014 Discrete Applied Mathematics  
On the algorithmic side, we show that the SEPI existence problem is NP-complete by reduction of SAT, and present a constraint satisfaction algorithm that has been successfully used to solve practical SEPI  ...  This problem is in turn equivalent to the existence of a subgraph (corresponding to delete operations) epimorphism (i.e. surjective homomorphism, corresponding to merge operations) from the first graph  ...  Graph matching problems can be easily modeled as constraint satisfaction problems [12] .  ... 
doi:10.1016/j.dam.2013.08.008 fatcat:t3ecsi2d5vaxxp4gyjcuxqfb4i

Beyond Boolean Surjective VCSPs

Gregor Matl, Stanislav Zivný, Michael Wagner
2019 Symposium on Theoretical Aspects of Computer Science  
Fulla, Uppman, and Živný [ACM ToCT '18] established a dichotomy theorem for Boolean surjective general-valued constraint satisfaction problems (VCSPs), i.e., VCSPs on two-element domains in which both  ...  We show that all near-optimal solutions to this problem can be enumerated in polynomial time, which might be of independent interest.  ...  Introduction Constraint satisfaction problems (CSPs) are fundamental computer science problems studied in artificial intelligence, logic (as model checking of the positive primitive fragment of first-order  ... 
doi:10.4230/lipics.stacs.2019.52 dblp:conf/stacs/MatlZ19 fatcat:mxwjycnib5hwlhfs3wkvs3upte

New Outer Bounds on the Marginal Polytope

David A. Sontag, Tommi S. Jaakkola
2007 Neural Information Processing Systems  
Finally, we demonstrate the advantage of the new constraints for finding the MAP assignment in protein structure prediction.  ...  We give a new class of outer bounds on the marginal polytope, and propose a cutting-plane algorithm for efficiently optimizing over these constraints.  ...  Acknowledgments The authors thank Amir Globerson and David Karger for helpful discussions. This work was supported in part by the DARPA Transfer Learning program.  ... 
dblp:conf/nips/SontagJ07 fatcat:upjsglbrkzg4lgv6ek4hd62ucq

Extending linear relaxation for non-square matrices and soft constraints

Noreen Jamil, Johannes Müller, M. Asif Naeem, Christof Lutteroth, Gerald Weber
2016 Journal of Computational and Applied Mathematics  
Linear relaxation is a common method for solving linear problems, as they occur in science and engineering.  ...  In contrast to direct methods such as Gausselimination or QR-factorization, linear relaxation is particularly efficient for problems with sparse matrices, as they appear in constraint-based user interface  ...  [58] proposed an algorithm, Diagnosis of Over-determined Constraint Satisfaction Problems.  ... 
doi:10.1016/j.cam.2016.05.006 fatcat:4k6byy6ogzghzi4u6ccxne3n3q

Page 1063 of Mathematical Reviews Vol. , Issue 95b [page]

1995 Mathematical Reviews  
Roth, Approximation algorithms for the vertex feed- back set problem with applications to constraint satisfaction and Bayesian inference (344-354); David P. Williamson and Michel X.  ...  Motogna, A recurrence method for computing the number of the surjective functions (37-44); D.  ... 

The Complexity of Approximately Counting Retractions [chapter]

Jacob Focke, Leslie Ann Goldberg, Stanislav Živný
2019 Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms  
We then show that the problem #Ret(H I v ,I e ) reduces to the #BIS-easy problem #CSP({Imp, δ 0 , δ 1 }). By choosing different instances I v and I e one can generate different #BIS-easiness results.  ...  It remains to show how to set up these instances to obtain the easiness result for partially bristled reflexive paths. This builds on the work of Kelk [31] .  ...  To this end, we cast the problem of counting downsets as a counting constraint satisfaction problem (CSP).  ... 
doi:10.1137/1.9781611975482.133 dblp:conf/soda/FockeGZ19 fatcat:5kbyvxtfr5erdf4ljei7ia4ary

Every Permutation CSP of arity 3 is Approximation Resistant

Moses Charikar, Venkatesan Guruswami, Rajsekar Manokaran
2009 2009 24th Annual IEEE Conference on Computational Complexity  
This is just the Maximum Acyclic Subgraph (MAS) problem.  ...  This is just the natural extension of constraint satisfaction problems over finite domains (such as Boolean CSPs) to the world of ordering problems.  ...  Keywords-hardness of approximation; betweenness; permutation constraint satisfaction problems; approximation resistance I.  ... 
doi:10.1109/ccc.2009.29 dblp:conf/coco/CharikarGM09 fatcat:paxbuwhb2nam7lmxcr7ntluw5m

Hard constraint satisfaction problems have hard gaps at location 1

Peter Jonsson, Andrei Krokhin, Fredrik Kuivinen
2009 Theoretical Computer Science  
An instance of the maximum constraint satisfaction problem (Max CSP) is a finite collection of constraints on a set of variables, and the goal is to assign values to the variables that maximises the number  ...  All constraint languages, for which the CSP problem (i.e., the problem of deciding whether all constraints can be satisfied) is currently known to be NP-hard, have a certain algebraic property.  ...  Acknowledgments The authors would like to thank Gustav Nordh for comments which have improved the presentation of this paper.  ... 
doi:10.1016/j.tcs.2009.05.022 fatcat:xqug66unprfcjfjlz4rbp23ar4

The Complexity of Approximately Counting Retractions [article]

Jacob Focke, Leslie Ann Goldberg, Stanislav Zivny
2018 arXiv   pre-print
--- whereas for exact counting all three of these problems are interreducible.  ...  We show that the problem of approximately counting retractions is separated both from the problem of approximately counting homomorphisms and from the problem of approximately counting list homomorphisms  ...  It is known that the counting constraint satisfaction problem is #BIS-equivalent when the constraint language contains (exactly) these three relations.  ... 
arXiv:1807.00590v2 fatcat:vhsn3wqpebegnees66jgcwl34u

Computationally Efficient Safe Reinforcement Learning for Power Systems [article]

Daniel Tabas, Baosen Zhang
2022 arXiv   pre-print
control or projection problem in real time.  ...  We also show that the proposed paradigm outperforms DDPG augmented with constraint violation penalties.  ...  Tabas would like to thank Liyuan Zheng for guidance and Sarah H.Q. Li for helpful discussions.  ... 
arXiv:2110.10333v2 fatcat:gz2jaawzuzapfbatxvjqbdtu7q

On the Approximation of Constrained Linear Quadratic Regulator Problems and their Application to Model Predictive Control - Supplementary Notes [article]

Michael Muehlebach, Raffaello D'Andrea
2018 arXiv   pre-print
By parametrizing input and state trajectories with basis functions different approximations to the constrained linear quadratic regulator problem are obtained.  ...  constraint sampling points: I 0 c = {t 1 , t 2 , . . . , t N }; maximum number of iterations: MAXITER; constraint satisfaction tolerance: ; 1: k = 0 2: for k <MAXITER do I k+1 c = I k c ∪ {t c }, k =  ...  The resulting approximations are given by convex finite-dimensional optimization problems that have a quadratic cost, linear equality constraints, and linear semi-infinite inequality constraints.  ... 
arXiv:1803.05510v1 fatcat:6nfj6wu6kjdspjj4jlojrkhwnq

Galois correspondence for counting quantifiers [article]

Andrei A. Bulatov, Amir Hedayaty
2012 arXiv   pre-print
Then we show that approximation preserving reductions between counting constraint satisfaction problems (#CSPs) are preserved by these two types of closure operators.  ...  While we were unable to identify a Galois correspondence for partial clones closed under max-implementation and max-quantification, we obtain such results for slightly different type of closure operators  ...  Satisfaction Problem (CSP, for short).  ... 
arXiv:1210.3344v1 fatcat:bli7tjoyivcmhidf2e3yt7icum
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