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Polynomial time approximation schemes for dense instances of minimum constraint satisfaction

2003
*
Random structures & algorithms (Print)
*

It is known that large fragments

doi:10.1002/rsa.10072
fatcat:nycnpgnlczbzxniyg4jgrhu2ni
*of*the class*of**dense**Minimum**Constraint**Satisfaction*(MIN-CSP) problems do not have*polynomial**time**approximation**schemes*(PTASs) contrary to their Maximum*Constraint*... In this paper we prove, somewhat surprisingly, that the*minimum**satisfaction**of**dense**instances**of*kSAT-formulas, and linear equations mod 2, Ek-LIN2, do have PTASs*for*any k. ... Acknowledgements 17 The authors thank Alan Frieze, Madhu Sudan, Mario Szegedy, and Luca Trevisan*for*stimulating remarks and discussions. ...##
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Page 5664 of Mathematical Reviews Vol. , Issue 2004g
[page]

2004
*
Mathematical Reviews
*

Among others, a fully

*polynomial*-*time**approximation**scheme*is presented*for*the case with one computing node. ... The result is interesting partly because these are examples*of**dense**minimum**constraint**satisfaction*prob- lems which are hard in general, and partly because*dense**minimum**constraint**satisfaction*problems ...##
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On the Complexity of Global Constraint Satisfaction
[chapter]

2005
*
Lecture Notes in Computer Science
*

We study the computational complexity

doi:10.1007/11602613_63
fatcat:gnteaqcrffezpedfx2zkote7am
*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. ... Thus, since Min Bisection has a*polynomial**time**approximation**scheme*on everywhere*instances*[AKK95], all the above problems have a*polynomial**time**approximation**scheme*on everywhere*dense**instances*. ...##
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Polynomial time approximation schemes for dense instances of NP-hard problems

1995
*
Proceedings of the twenty-seventh annual ACM symposium on Theory of computing - STOC '95
*

. 1 have a fully

doi:10.1145/225058.225140
dblp:conf/stoc/AroraKK95
fatcat:c3kolvccwbee7lzlxc457jizmy
*polynomial**time**approximation**scheme*. ... We present a unified framework*for*designing*polynomial**time**approximation**schemes*(PTASs)*for*"*dense*"*instances**of*many N P-hard optimization problems, including maximum cut, graph bisection, graph separation ... (An alternative name*for*MAX-k-FUNCTION-SAT is "*constraint**satisfaction*problems" [KSW97] . ) We call an*instance**of*a MAX-SN P 0 problem*dense*if the*instance**of*MAX-k-FUNCTION-SAT produced using it ...##
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Approximability of the Minimum Bisection Problem: An Algorithmic Challenge
[chapter]

2002
*
Lecture Notes in Computer Science
*

We survey some recent results on the complexity

doi:10.1007/3-540-45687-2_4
fatcat:k7art7ukvrgshkquf65he4juha
*of*computing*approximate*solutions*for**instances**of*the*Minimum*Bisection problem and formulate some very intriguing and still open questions about the*approximability*... status*of*that problem. ... Fernandez de la Vega, Ravi Kannan, and Claire Kenyon*for*many stimulating discussions. ...##
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The approximability of NP-hard problems

1998
*
Proceedings of the thirtieth annual ACM symposium on Theory of computing - STOC '98
*

A

doi:10.1145/276698.276784
dblp:conf/stoc/Arora98
fatcat:yu5xnmrhsbd2xk7m6aanrb5ule
*polynomial**time**approximation**scheme*or PTAS is an algorithm that,*for*any fixed > 0, can achieve an*approximation*ratio 1 + in*time*that is*polynomial*in the input size. ... A fully*polynomial**time**approximation**scheme*or FPTAS is an algorithm that, given input x and error bound > 0, computes a solution*of*cost at most (1 + )OP T in*time*that is*polynomial*in |x| and 1/ . ...##
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Hardness of fully dense problems

2007
*
Information and Computation
*

In the past decade, there has been a stream

doi:10.1016/j.ic.2007.02.006
fatcat:23v63btifrastnpzt4td5wsh3y
*of*work in designing*approximation**schemes**for**dense**instances**of*NP-Hard problems. ... In this work, we prove hardness results*of**dense**instances**of*a broad family*of*CSP problems, as well as a broad family*of*ranking problems which we refer to as CSP-Rank. ... Acknowledgment We thank Moses Charikar*for*helpful discussions. ...##
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Tensor decomposition and approximation schemes for constraint satisfaction problems

2005
*
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing - STOC '05
*

The only general class

doi:10.1145/1060590.1060701
dblp:conf/stoc/VegaKKV05
fatcat:7cq23vvqljddrepbxunm2gxt44
*of*MAX-rCSP problems*for*which*Polynomial**Time**Approximation**Schemes*(PTAS) are known are the*dense*problems. ... In this paper, we give PTAS's*for*a much larger class*of*weighted MAX-rCSP problems which includes as special cases the*dense*problems and,*for*r = 2, all metric*instances*(where the weights satisfy the ... As a consequence,*for*any MAX-rCSP that satisfies a certain density condition, we obtain a*polynomial*-*time**approximation**scheme*. ...##
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How to Round Any CSP

2009
*
2009 50th Annual IEEE Symposium on Foundations of Computer Science
*

A large number

doi:10.1109/focs.2009.74
dblp:conf/focs/RaghavendraS09a
fatcat:ctrylxuxafdvhkimo3vjwyits4
*of*interesting combinatorial optimization problems like M C, M k-S, and U G fall under the class*of**constraint**satisfaction*problems (CSPs). ... In this work, we present an efficient rounding*scheme*that achieves the integrality gap*of*this basic SDP relaxation*for*every CSP (and by [33] it also achieves the gap*of*much stronger SDP relaxations ... Theorem 1.1:*For*every CSP Λ and*for*every ε > 0, there exists a*polynomial**time**approximation*algorithm*for*Λ-CSP that returns an assignment*of*value at least S Λ (c − ε) − ε on an*instance*Φ with SDP ...##
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Approximation Algorithms for NP-Hard Problems

2004
*
Oberwolfach Reports
*

lower bounds

doi:10.4171/owr/2004/28
fatcat:fwbs36pgpjev5gk6cfeb7ylukm
*for*efficient*approximation*. ... An important mean*for*surmounting this intractability barrier is that*of**approximate*computation, where the answer is guaranteed to be within some small fraction*of*optimality. ...*Polynomial**Time**Approximation**Schemes**for*Some*Dense**Instances**of*NP-Hard Problems. Algorithmica 30 (2001), pp. 386-397. [RZ00a] G. Robins and A. Zelikovsky. ...##
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An information-based neural approach to generic constraint satisfaction

2002
*
Artificial Intelligence
*

A novel artificial neural network heuristic (INN)

doi:10.1016/s0004-3702(02)00291-6
fatcat:x42fipv66bhwxbpl54sc5dwqna
*for*general*constraint**satisfaction*problems is presented, extending a recently suggested method restricted to boolean variables. ... In contrast to conventional ANN methods, it employs a particular type*of*non-*polynomial*cost function, based on the information balance between variables and*constraints*in a mean-field setting. ... Peterson*for*stimulating discussions. This work was in part supported by the Swedish Foundation*for*Strategic Research. ...##
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On Weighted vs Unweighted Versions of Combinatorial Optimization Problems

2001
*
Information and Computation
*

*For*an appropriate (and very general) definition

*of*niceness, we show that if a nice weighted problem is hard to

*approximate*within r , then its

*polynomially*bounded weighted version is hard to

*approximate*... These reductions give new non-

*approximability*results

*for*these problems. ... ACKNOWLEDGMENTS We thank Viggo Kann

*for*having read a preliminary version

*of*this paper and

*for*suggesting some useful modifications. ...

##
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Voting algorithms for unique games on complete graphs
[article]

2021
*
arXiv
*
pre-print

An

arXiv:2110.11851v1
fatcat:xfppdrj5tff23ipvezlljtzfd4
*approximation*algorithm*for*a*Constraint**Satisfaction*Problem is called robust if it outputs an assignment satisfying a (1 - f(ϵ))-fraction*of*the*constraints*on any (1-ϵ)-satisfiable*instance*, where ... The runtime*of*our algorithm is O(qn^3) (with no dependence on ϵ) and can run in*time*O(qn^2) using a randomized implementation with a slightly larger constant c_ϵ. ... In order to obtain a (randomized)*polynomial*-*time**approximation**scheme*(PTAS)*for*Min-Unique-Games(q)-Full we rely on the following theorem, where we emphasize that q is considered a constant (i.e., the ...##
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Linear Time Approximation Schemes for the Gale-Berlekamp Game and Related Minimization Problems
[article]

2008
*
arXiv
*
pre-print

We design a linear

arXiv:0811.3244v1
fatcat:z72vlu7ijfhepidrhegmiz5uau
*time**approximation**scheme**for*the Gale-Berlekamp Switching Game and generalize it to a wider class*of**dense*fragile minimization problems including the Nearest Codeword Problem (NCP) ... As another application*of*our method we give the first linear*time**approximation**schemes**for*correlation clustering with a fixed number*of*clusters and its hierarchical generalization. ... Acknowledgements We would like to thank Claire Mathieu and Joel Spencer*for*raising a question on*approximability*status*of*the Gale-Berlekamp game and Alex Samorodintsky*for*interesting discussions ...##
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Sensor-mission assignment in wireless sensor networks

2010
*
ACM transactions on sensor networks
*

We propose algorithms

doi:10.1145/1777406.1777415
fatcat:q5etoy6qxradvgih6o7fjinmhi
*for*the different variants, some*of*which include*approximation*guarantees. ...*Schemes*that assign sensing resources to missions thus become necessary. In this article, we formally define the sensor-mission assignment problem and discuss some*of*its variants. ... We would also like to thank the anonymous reviewers*for*their valuable comments. ...
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