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Polynomial time approximation schemes for dense instances of minimum constraint satisfaction

Cristina Bazgan, W. Fernandez de la Vega, Marek Karpinski
2003 Random structures & algorithms (Print)  
It is known that large fragments 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.  ... 
doi:10.1002/rsa.10072 fatcat:nycnpgnlczbzxniyg4jgrhu2ni

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  ... 

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.  ...  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.  ... 
doi:10.1007/11602613_63 fatcat:gnteaqcrffezpedfx2zkote7am

Polynomial time approximation schemes for dense instances of NP-hard problems

Sanjeev Arora, David Karger, Marek Karpinski
1995 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing - STOC '95  
. 1 have a fully 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  ... 
doi:10.1145/225058.225140 dblp:conf/stoc/AroraKK95 fatcat:c3kolvccwbee7lzlxc457jizmy

Approximability of the Minimum Bisection Problem: An Algorithmic Challenge [chapter]

Marek Karpinski
2002 Lecture Notes in Computer Science  
We survey some recent results on the complexity 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.  ... 
doi:10.1007/3-540-45687-2_4 fatcat:k7art7ukvrgshkquf65he4juha

The approximability of NP-hard problems

Sanjeev Arora
1998 Proceedings of the thirtieth annual ACM symposium on Theory of computing - STOC '98  
A 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/ .  ... 
doi:10.1145/276698.276784 dblp:conf/stoc/Arora98 fatcat:yu5xnmrhsbd2xk7m6aanrb5ule

Hardness of fully dense problems

Nir Ailon, Noga Alon
2007 Information and Computation  
In the past decade, there has been a stream 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.  ... 
doi:10.1016/j.ic.2007.02.006 fatcat:23v63btifrastnpzt4td5wsh3y

Tensor decomposition and approximation schemes for constraint satisfaction problems

W. Fernandez de la Vega, Marek Karpinski, Ravi Kannan, Santosh Vempala
2005 Proceedings of the thirty-seventh annual ACM symposium on Theory of computing - STOC '05  
The only general class 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.  ... 
doi:10.1145/1060590.1060701 dblp:conf/stoc/VegaKKV05 fatcat:7cq23vvqljddrepbxunm2gxt44

How to Round Any CSP

Prasad Raghavendra, David Steurer
2009 2009 50th Annual IEEE Symposium on Foundations of Computer Science  
A large number 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  ... 
doi:10.1109/focs.2009.74 dblp:conf/focs/RaghavendraS09a fatcat:ctrylxuxafdvhkimo3vjwyits4

Approximation Algorithms for NP-Hard Problems

Ravindran Kannan, Marek Karpinski
2004 Oberwolfach Reports  
lower bounds 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.  ... 
doi:10.4171/owr/2004/28 fatcat:fwbs36pgpjev5gk6cfeb7ylukm

An information-based neural approach to generic constraint satisfaction

Henrik Jönsson, Bo Söderberg
2002 Artificial Intelligence  
A novel artificial neural network heuristic (INN) 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.  ... 
doi:10.1016/s0004-3702(02)00291-6 fatcat:x42fipv66bhwxbpl54sc5dwqna

On Weighted vs Unweighted Versions of Combinatorial Optimization Problems

Pierluigi Crescenzi, Riccardo Silvestri, Luca Trevisan
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.  ... 
doi:10.1006/inco.2000.3011 fatcat:pqvgcjfopjdxfnbaar67uhcuda

Voting algorithms for unique games on complete graphs [article]

Antoine Méot and Arnaud de Mesmay and Moritz Mühlenthaler and Alantha Newman
2021 arXiv   pre-print
An 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  ... 
arXiv:2110.11851v1 fatcat:xfppdrj5tff23ipvezlljtzfd4

Linear Time Approximation Schemes for the Gale-Berlekamp Game and Related Minimization Problems [article]

Marek Karpinski, Warren Schudy
2008 arXiv   pre-print
We design a linear 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  ... 
arXiv:0811.3244v1 fatcat:z72vlu7ijfhepidrhegmiz5uau

Sensor-mission assignment in wireless sensor networks

Hosam Rowaihy, Matthew P. Johnson, Ou Liu, Amotz Bar-Noy, Theodore Brown, Thomas La Porta
2010 ACM transactions on sensor networks  
We propose algorithms 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.  ... 
doi:10.1145/1777406.1777415 fatcat:q5etoy6qxradvgih6o7fjinmhi
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