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A Dichotomy Theorem for the Resolution Complexity of Random Constraint Satisfaction Problems

Siu On Chan, Michael Molloy
2013 SIAM journal on computing (Print)  
We consider random instances of constraint satisfaction problems where each variable has domain size O(1), each constraint is on O(1) variables and the constraints are chosen from a specified distribution  ...  Achlioptas et al [2] began with the easy observation that random (2 + p)-SAT, a mixture of random 2-SAT and random 3-SAT has polynomial resolution complexity if the number of clauses is so high that the  ...  Acknowledgement We would like to thank anonymous referees and Toniann Pitassi for helpful comments on an earlier draft of this paper.  ... 
doi:10.1137/110832240 fatcat:52ewoojeefbfthsz7mnnmcdhqm

A Dichotomy Theorem for the Resolution Complexity of Random Constraint Satisfaction Problems

Siu On Chan, Michael Molloy
2008 2008 49th Annual IEEE Symposium on Foundations of Computer Science  
We consider random instances of constraint satisfaction problems where each variable has domain size O(1), each constraint is on O(1) variables and the constraints are chosen from a specified distribution  ...  Achlioptas et al [2] began with the easy observation that random (2 + p)-SAT, a mixture of random 2-SAT and random 3-SAT has polynomial resolution complexity if the number of clauses is so high that the  ...  Acknowledgement We would like to thank anonymous referees and Toniann Pitassi for helpful comments on an earlier draft of this paper.  ... 
doi:10.1109/focs.2008.70 dblp:conf/focs/ChanM08 fatcat:7l2q37573fcsne6ip74i7clfce

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

Counting Problems and Clones of Functions

Andrei A. Bulatov
2009 2009 39th International Symposium on Multiple-Valued Logic  
The Counting Constraint Satisfaction Problem (#CSP for short) provides a powerful yet convenient formalism to express counting problems.  ...  The central question in this area is the complexity of and algorithms for problems of this type.  ...  This question (similar questions also arise for other types of constraint satisfaction problems), or rather a positive resolution of it, are known as dichotomy conjecture for counting problems.  ... 
doi:10.1109/ismvl.2009.47 dblp:conf/ismvl/Bulatov09 fatcat:4xtyqeumsvbr3lcnfu4ukzfrsy

Phase Transitions and all that [article]

Gabriel Istrate
2005 arXiv   pre-print
It has been subsequently split into two papers, the corrected (and accepted for publication) versions appear in the archive as papers cs.CC/0503082 and cs.DM/0503083.  ...  The paper (as posted originally) contains several errors.  ...  The proof of Claim 6 (and of item 2. of Theorem 5) follows: since for any clause K of one of the original constraints µ(K) = 1, since µ( ) > η 1 · n and since w.l.o.g. 0 < d < η 1 (otherwise replace d  ... 
arXiv:cs/0211012v2 fatcat:ojkdnqvi4jhrzlqclksqqnnvym

A new line of attack on the dichotomy conjecture

Gábor Kun, Mario Szegedy
2009 Proceedings of the 41st annual ACM symposium on Symposium on theory of computing - STOC '09  
The resolution of this conjecture would be a major step towards the resolution of the dichotomy conjecture.  ...  The well known dichotomy conjecture of Feder and Vardi states that for every family Γ of constraints CSP(Γ) is either polynomially solvable or NP-hard.  ...  Introduction Constraint satisfaction problems (CSP) are the pinnacles in N P not only because they have multiple interpretations in logic, combinatorics, and complexity theory, but also for their immense  ... 
doi:10.1145/1536414.1536512 dblp:conf/stoc/KunS09 fatcat:6dty6pbagzbj5ovmsjkia72724

A new line of attack on the dichotomy conjecture

Gábor Kun, Mario Szegedy
2016 European journal of combinatorics (Print)  
The resolution of this conjecture would be a major step towards the resolution of the dichotomy conjecture.  ...  The well known dichotomy conjecture of Feder and Vardi states that for every family Γ of constraints CSP(Γ) is either polynomially solvable or NP-hard.  ...  Introduction Constraint satisfaction problems (CSP) are the pinnacles in N P not only because they have multiple interpretations in logic, combinatorics, and complexity theory, but also for their immense  ... 
doi:10.1016/j.ejc.2015.07.011 fatcat:fg6zuisfbvgkpkh6cnt23xm7hq

An approximation trichotomy for Boolean #CSP

Martin Dyer, Leslie Ann Goldberg, Mark Jerrum
2010 Journal of computer and system sciences (Print)  
We give a trichotomy theorem for the complexity of approximately counting the number of satisfying assignments of a Boolean CSP instance.  ...  This means that the problem of approximately counting satisfying assignments of such a CSP instance is equivalent in complexity to several other known counting problems, including the problem of approximately  ...  Understanding the complexity of constraint satisfaction problems has become a major and active area within computational complexity [7, 11] .  ... 
doi:10.1016/j.jcss.2009.08.003 fatcat:sod7lmaym5eg7kz34bmg4hpk6e

On the Minimal Constraint Satisfaction Problem: Complexity and Generation [chapter]

Guillaume Escamocher, Barry O'Sullivan
2015 Lecture Notes in Computer Science  
Our complexity result can be seen as providing a dichotomy theorem for the Minimal CSP.  ...  The Minimal Constraint Satisfaction Problem, or Minimal CSP for short, arises in a number of real-world applications, most notably in constraint-based product configuration.  ...  This publication has emanated from research conducted with the financial support of Science Foundation Ireland (SFI) under Grant Number SFI/12/RC/2289.  ... 
doi:10.1007/978-3-319-26626-8_54 fatcat:vwyxrzbhojacxnoriybchxiohe

Sparse Combinatorial Structures: Classification and Applications

Jaroslav Nešetřil, Patrice Ossona de Mendez
2011 Proceedings of the International Congress of Mathematicians 2010 (ICM 2010)  
The topics include: complexity of subgraph-and homomorphism-problems; model checking problems for first order formulas in special classes; property testing in sparse classes of structures.  ...  All these problems can be studied under the umbrella of classes of structures which are Nowhere Dense and in the context of Nowhere Dense -Somewhere Dense dichotomy.  ...  We list the following areas as related to this paper: • universal and generic structures of model theory; • Constraint Satisfaction Problems in the context of descriptive complexity; • complexity of subgraph-and  ... 
doi:10.1142/9789814324359_0156 fatcat:io4dnuj4wzarvest64wnvvm4ge

An approximation trichotomy for Boolean #CSP [article]

Martin Dyer, Leslie Ann Goldberg, Mark Jerrum
2009 arXiv   pre-print
We give a trichotomy theorem for the complexity of approximately counting the number of satisfying assignments of a Boolean CSP instance.  ...  This means that the problem of approximately counting satisfying assignments of such a CSP instance is equivalent in complexity to several other known counting problems, including the problem of approximately  ...  Understanding the complexity of constraint satisfaction problems has become a major and active area within computational complexity [7, 11] .  ... 
arXiv:0710.4272v2 fatcat:dxdbyt357jg4refsyexdkzf3fi

Complexity of Constraint Languages [chapter]

2013 Qualitative Spatial and Temporal Reasoning  
One of the most fundamental challenges in constraint programming is to understand the computational complexity of problems involving constraints.  ...  It has been shown that the class of all constraint satisfaction problem instances is NP-hard [71] , so it is unlikely that efficient general-purpose algorithms exist for solving all forms of constraint  ...  Similar dichotomy results have also been obtained for many other combinatorial problems over a Boolean domain which are related to the Boolean constraint satisfaction problem [62, 27] . Example 6.  ... 
doi:10.1002/9781118601457.ch12 fatcat:7j7hws3cuvflnc7kn5svtfpmqe

The Complexity of Constraint Languages [chapter]

David Cohen, Peter Jeavons
2006 Foundations of Artificial Intelligence  
One of the most fundamental challenges in constraint programming is to understand the computational complexity of problems involving constraints.  ...  It has been shown that the class of all constraint satisfaction problem instances is NP-hard [71] , so it is unlikely that efficient general-purpose algorithms exist for solving all forms of constraint  ...  Similar dichotomy results have also been obtained for many other combinatorial problems over a Boolean domain which are related to the Boolean constraint satisfaction problem [62, 27] . Example 6.  ... 
doi:10.1016/s1574-6526(06)80012-x fatcat:ddy7y6xwknhjvbsnblkonm6iku

Randomization in Parameterized Complexity (Dagstuhl Seminar 17041)

Marek Cygan, Fedor V. Fomin, Danny Hermelin, Magnus Wahlström, Marc Herbstritt
2017 Dagstuhl Reports  
Dagstuhl Seminar 17041 "Randomization in Parameterized Complexity" took place from January 22nd to January 27th 2017 with the objective to bridge the gap between randomization and parameterized complexity  ...  This report documents the talks held during the seminar as well as the open questions arised in the discussion sessions.  ...  More precisely, we prove that Minimum Spanning Circuit parameterized by |T | is W [1] -hard even on cographic matroids, a proper subclass of regular matroids.  ... 
doi:10.4230/dagrep.7.1.103 dblp:journals/dagstuhl-reports/CyganFHW17 fatcat:vjbkuavqdzew3nbk6wjvmpbd5m

Connectivity of Boolean Satisfiability [article]

Konrad W. Schwerdtfeger
2015 arXiv   pre-print
(as considered in Schaefer's famous 1978 dichotomy theorem); we prove a computational dichotomy for the st-connectivity problem, asserting that it is either solvable in polynomial time or PSPACE-complete  ...  for the connectivity problem, we show a trichotomy in the case of quantified formulas, while in the case of formulas without constants, we identify fragments of a possible trichotomy.  ...  Thomas Schaefer introduced CNF(S)-formulas for expressing variants of Boolean satisfiability; in his dichotomy theorem, Schaefer then classified the complexity of the satisfiability problem for CNF C (  ... 
arXiv:1510.06700v1 fatcat:4fwr3m2l4fbrhdycknubsjz74q
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