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

2013
*
arXiv
*
pre-print

We show improved

arXiv:1307.5090v1
fatcat:zqz7tffqbvhklbroaryxeobpxe
*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. ...##
###
Treewidth and the Computational Complexity of MAP Approximations
[chapter]

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*. ...

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

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 ...

##
###
Approximation for Maximum Surjective Constraint Satisfaction Problems
[article]

2011
*
arXiv
*
pre-print

Maximum surjective

arXiv:1110.2953v1
fatcat:gdfk7mfaengyjnscr4ljrau5b4
*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 ...##
###
Tree-Width and the Computational Complexity of MAP Approximations in Bayesian Networks

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). ...

##
###
Universal Factor Graphs for Every NP-Hard Boolean CSP

2014
*
International Workshop on Approximation Algorithms for Combinatorial Optimization
*

Depending

doi:10.4230/lipics.approx-random.2014.274
dblp:conf/approx/Jozeph14
fatcat:debsvkobh5dunpnxslbeoiaowy
*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). ...##
###
The Constraint Satisfaction Problem: Complexity and Approximability (Dagstuhl Seminar 15301)

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*. ...

##
###
On the Complexity of Global Constraint Satisfaction
[chapter]

2005
*
Lecture Notes in Computer Science
*

We study

doi:10.1007/11602613_63
fatcat:gnteaqcrffezpedfx2zkote7am
*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*. ...##
###
Optimal Approximation Algorithms for Reoptimization of Constraint Satisfaction Problems

2013
*
American Journal of Operations Research
*

For this

doi:10.4236/ajor.2013.32025
fatcat:5xfdwbnbvrcv7ohnnwnwos6qoa
*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*...##
###
Max NP-completeness made easy

1999
*
Theoretical Computer Science
*

Successively, we show that

doi:10.1016/s0304-3975(98)00200-x
fatcat:w76vu5nmqvgwrhxoiaqykoz44e
*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. ...##
###
The approximability of NP-hard problems

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. ...

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

2005
*
Lecture Notes in Computer Science
*

Our results show that

doi:10.1007/11538462_9
fatcat:4v2m7huchvcodgvi3k374voz5y
*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. ...##
###
Identifying Efficiently Solvable Cases of Max CSP
[chapter]

2004
*
Lecture Notes in Computer Science
*

In this paper we study

doi:10.1007/978-3-540-24749-4_14
fatcat:k2fq6aljyzan3e2hn376u6zley
*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. ...##
###
Forthcoming papers

1997
*
Artificial Intelligence
*

Our experiments

doi:10.1016/s0004-3702(97)90018-7
fatcat:a35n37e5tfdwbeogondihqahey
*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. ...##
###
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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