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On the NP-Hardness of Approximating Ordering Constraint Satisfaction Problems [article]

Per Austrin and Rajsekar Manokaran and Cenny Wenner
2013 arXiv   pre-print
We show improved NP-hardness of approximating Ordering Constraint Satisfaction Problems (OCSPs).  ...  An OCSP is said to be approximation resistant if it is hard to approximate better than taking a uniformly random ordering.  ...  We would like to thank Johan Håstad for suggesting this problem and for numerous helpful discussions regarding the same.  ... 
arXiv:1307.5090v1 fatcat:zqz7tffqbvhklbroaryxeobpxe

Treewidth and the Computational Complexity of MAP Approximations [chapter]

Johan Kwisthout
2014 Lecture Notes in Computer Science  
The problem of finding the most probable explanation to a designated set of variables (the MAP problem) is a notoriously intractable problem in Bayesian networks, both to compute exactly and to approximate  ...  We prove that efficient value-, structure-, and rank-approximations of MAP instances with high treewidth will violate the Exponential Time Hypothesis.  ...  Hence, any structure-approximation algorithm that can correctly return the value of one of the variables in H, effectively solves Constraint Satisfaction.  ... 
doi:10.1007/978-3-319-11433-0_18 fatcat:klmitw6wsfg27htqx6uemrbxdu

The Constraint Satisfaction Problem: Complexity and Approximability (Dagstuhl Seminar 18231)

Martin Grohe, Venkatesan Guruswami, Stanislav Zivny, Michael Wagner
2018 Dagstuhl Reports  
Constraint satisfaction has always played a central role in computational complexity theory; appropriate versions of CSPs are classical complete problems for most standard complexity classes.  ...  CSPs constitute a very rich and yet sufficiently manageable class of problems to give a good perspective on general computational phenomena.  ...  -The Constraint Satisfaction Problem: Complexity and Approximability From Weak to Strong LP Gaps for all CSPs We study the approximability of constraint satisfaction problems (CSPs) by linear programming  ... 
doi:10.4230/dagrep.8.6.1 dblp:journals/dagstuhl-reports/GroheGZ18 fatcat:3bqo62ly3rgzlnh3bmkvwbuwea

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  ...  A solution to such a problem is a surjective mapping from the set of variables to B such that the number of satisfied constraints is maximized.  ...  Introduction The constraint satisfaction problem (CSP) is an important computational problem in NP where the task is to decide whether there exists a homomor-phism from a given input relational structure  ... 
arXiv:1110.2953v1 fatcat:gdfk7mfaengyjnscr4ljrau5b4

Tree-Width and the Computational Complexity of MAP Approximations in Bayesian Networks

Johan Kwisthout
2015 The Journal of Artificial Intelligence Research  
The problem of finding the most probable explanation to a designated set of variables given partial evidence (the MAP problem) is a notoriously intractable problem in Bayesian networks, both to compute  ...  We introduce the complexity class FERT, analogous to the class FTP, to capture this notion of fixed-parameter expectation-approximability.  ...  Acknowledgements A previous version of this paper (Kwisthout, 2014) was published in the Proceedings of the Seventh European Workshop on Probabilistic Graphical Models (PGM 2014).  ... 
doi:10.1613/jair.4794 fatcat:6z4vmygryfhudf46rmfhlrb67i

Universal Factor Graphs for Every NP-Hard Boolean CSP

Shlomo Jozeph, Marc Herbstritt
2014 International Workshop on Approximation Algorithms for Combinatorial Optimization  
Depending on the allowed choices of constraints, it is known that Boolean constraint satisfaction problems fall into one of two classes, being either NP-hard or in P.  ...  That is, for every NP-hard Boolean constraint satisfaction problem, there is a family of at most one factor graph of each size, such that the problem, restricted to instances that have a factor graph from  ...  Work supported in part by the Israel Science Foundation (grant No. 621/12).  ... 
doi:10.4230/lipics.approx-random.2014.274 dblp:conf/approx/Jozeph14 fatcat:debsvkobh5dunpnxslbeoiaowy

The Constraint Satisfaction Problem: Complexity and Approximability (Dagstuhl Seminar 15301)

Andrei A. Bulatov, Venkatesan Guruswami, Andrei Krokhin, Dániel Marx, Marc Herbstritt
2016 Dagstuhl Reports  
The Dagstuhl Seminar 15301 "The Constraint Satisfaction Problem: Complexity and Approximability" was aimed at bringing together researchers using all the different techniques in the study of the CSP, so  ...  combinatorics, have been used to analyze both the computational complexity and approximabilty of algorithmic tasks related to the constraint satisfaction problem (CSP), as well as the applicability/limitations  ...  The use of approximation algorithms is one of the most fruitful approaches to coping with NP-hardness.  ... 
doi:10.4230/dagrep.5.7.22 dblp:journals/dagstuhl-reports/BulatovGKM15 fatcat:lcyvfsxsbzbrfe27irlpxepxoi

On the Complexity of Global Constraint Satisfaction [chapter]

Cristina Bazgan, Marek Karpinski
2005 Lecture Notes in Computer Science  
We study the computational complexity of decision and optimization problems that may be expressed as boolean contraint satisfaction problem with the global cardinality constraints.  ...  In this paper we establish a characterization theorem for the decision problems and derive approximation hardness results for the corresponding global optimization problems.  ...  In this paper we study the complexity of decision and optimization problems of the balanced versions of boolean constraint satisfaction problems depending on the type of constraints.  ... 
doi:10.1007/11602613_63 fatcat:gnteaqcrffezpedfx2zkote7am

Optimal Approximation Algorithms for Reoptimization of Constraint Satisfaction Problems

Victor Alex Mikhailyuk
2013 American Journal of Operations Research  
For this problem there is the name of inapproximability or the hardness of approximation.  ...  To solve the problem Ins-Max-EkCSP-P (reoptimization of Max-EkCSP-P with the addition of one constraint) with approximation resistant predicate P exists a poly- bounds for the complexity) is a very difficult  ...  The essence of the criterion for the most of NP-hard problems is that in order to show NPhardness of reoptimization versions suggestions are based on polynomial Turing reducibility of the original problem  ... 
doi:10.4236/ajor.2013.32025 fatcat:5xfdwbnbvrcv7ohnnwnwos6qoa

Max NP-completeness made easy

Pierluigi Crescenzi, Luca Trevisan
1999 Theoretical Computer Science  
Successively, we show that the "planar" restrictions of several optimization constraint satisfaction problems admit linear-time approximation schemes (thus improving the results of Khanna and Motwani,  ...  We introduce a simple technique to obtain reductions between optimization constraint satisfaction problems with respect to an approximation preserving redu~ibil~~ more powerful than the commonly used L-reduc  ...  We prove that for any r and any r' <r, the existence of an r'-approximate algorithm for MAX k(n)SAT implies the existence of an ~-approximate algorithm for MAX SAT.  ... 
doi:10.1016/s0304-3975(98)00200-x fatcat:w76vu5nmqvgwrhxoiaqykoz44e

The approximability of NP-hard problems

Sanjeev Arora
1998 Proceedings of the thirtieth annual ACM symposium on Theory of computing - STOC '98  
Constraint Satisfaction Problems A constraint satisfaction problem consists of c boolean functions f 1 , . . . , f c of arity at most k, where c, k are some constants.  ...  A classical result of Schaefer [119] shows that each constraint satisfaction problem is either in P or NP-complete.  ... 
doi:10.1145/276698.276784 dblp:conf/stoc/Arora98 fatcat:yu5xnmrhsbd2xk7m6aanrb5ule

The Complexity of Making Unique Choices: Approximating 1-in-k SAT [chapter]

Venkatesan Guruswami, Luca Trevisan
2005 Lecture Notes in Computer Science  
Our results show that the 1in-kSAT problem exhibits some rather peculiar phenomena in the realm of constraint satisfaction problems.  ...  We study the approximability of 1-in-kSAT, the variant of Max kSAT where a clause is deemed satisfied when precisely one of its literals is satisfied.  ...  Acknowledgments We would like to thank Chris Chang for his proof of Lemma 6 and Ziv Bar-Yossef for useful discussions.  ... 
doi:10.1007/11538462_9 fatcat:4v2m7huchvcodgvi3k374voz5y

Identifying Efficiently Solvable Cases of Max CSP [chapter]

David Cohen, Martin Cooper, Peter Jeavons, Andrei Krokhin
2004 Lecture Notes in Computer Science  
In this paper we study the complexity of the maximum constraint satisfaction problem (Max CSP) over an arbitrary finite domain.  ...  Using this connection, we are able to identify large classes of efficiently solvable subproblems of Max CSP arising from certain restrictions on the constraint types.  ...  One possible direction to extend our results would be a further study of the approximability of constraint satisfaction problems over arbitrary finite domains.  ... 
doi:10.1007/978-3-540-24749-4_14 fatcat:k2fq6aljyzan3e2hn376u6zley

Forthcoming papers

1997 Artificial Intelligence  
Our experiments on hard problems in the transition region show that LPC has the best effectiveness-efficiency tradeoff for processing TCSPs.  ...  Processing disjunctions in temporal constraint networks Temporal constraint satisfaction problems (TCSPs) provide a formal framework for representing and processing temporal knowledge.  ...  This paper proposes a definition of finite-domain constraint satisfaction problems with bilevel constraints in order to take into account a many to one relation between the values and the variables.  ... 
doi:10.1016/s0004-3702(97)90018-7 fatcat:a35n37e5tfdwbeogondihqahey

Page 7062 of Mathematical Reviews Vol. , Issue 2003i [page]

2003 Mathematical Reviews  
) by using a specialization of the criteria introduced by Schaefer in order to classify con- straint satisfaction problems and subsequently used by Khanna, Sudan, Trevisan, and Williamson to classify constraint  ...  [Rossi, Gianluca] (I-FRNZ-I; Florence) On the Hamming distance of constraint satisfaction problems. (English summary) Complexity and logic (Vienna, 1998). Theoret. Comput.  ... 
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