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Complexity and Approximability of Parameterized MAX-CSPs

Holger Dell, Eun Jung Kim, Michael Lampis, Valia Mitsou, Tobias Mömke
2017 Algorithmica  
We study the optimization version of constraint satisfaction problems (Max-CSPs) in the framework of parameterized complexity; the goal is to compute the maximum fraction of constraints that can be satisfied  ...  We consider Max-CSPs with the constraint types AND, OR, PARITY, and MAJORITY, and with various parameters k, and we attempt to fully classify them into the following three cases: 1.  ...  There exists an FPT-AS which, given > 0 and an instance φ of MAX-THRESHOLD, computes a (1 − )-approximate solution and runs in time f (fvs * , ) · poly(n), where fvs * is the size of the smallest feedback  ... 
doi:10.1007/s00453-017-0310-8 fatcat:ofab3wvgwjg75kehvxwaecmytm

Constraint Satisfaction Problems Parameterized Above or Below Tight Bounds: A Survey [article]

G. Gutin, A. Yeo
2011 arXiv   pre-print
We also consider Max-r-CSP-AA, a natural generalization of both Max-r-Lin2-AA and Max-r-Sat-AA, order (or, permutation) constraint satisfaction problems of arities 2 and 3 parameterized above the average  ...  is the parameter, r_i is the number of literals in Clause i, and r is a constant).  ...  Parameterized complexity of Ordering CSPs of arities 4 and higher is still unknown.  ... 
arXiv:1108.4803v1 fatcat:3wxkx7blgjfkzmqtw4jn7qdlqa

Constraint Satisfaction Problems Parameterized above or below Tight Bounds: A Survey [chapter]

Gregory Gutin, Anders Yeo
2012 Lecture Notes in Computer Science  
We also consider Max-r-CSP-AA, a natural generalization of both Max-r-Lin2-AA and Max-r-Sat-AA, order (or, permutation) constraint satisfaction problems of arities 2 and 3 parameterized above the average  ...  , where k is the parameter, ri is the number of literals in Clause i, and r is a constant).  ...  Parameterized complexity of Ordering CSPs of arities 4 and higher is still unknown.  ... 
doi:10.1007/978-3-642-30891-8_14 fatcat:r6ztg5kqybefhfxd2myyxtbq6q

Experimental Evaluation of Parameterized Algorithms for Graph Separation Problems: Half-Integral Relaxations and Matroid-based Kernelization [article]

Marcin Pilipczuk, Michał Ziobro
2018 arXiv   pre-print
In the recent years we have witnessed a rapid development of new algorithmic techniques for parameterized algorithms for graph separation problems.  ...  We present experimental evaluation of two cornerstone theoretical results in this area: linear-time branching algorithms guided by half-integral relaxations and kernelization (preprocessing) routines based  ...  Recall that in parameterized complexity, an instance x of a studied problem comes up with an integer parameter k which is supposed to measure the complexity of the instance.  ... 
arXiv:1811.07779v1 fatcat:w2q6qjlupffujot5op7zkqywey

Optimal Polynomial-Time Compression for Boolean Max CSP

Bart M. P. Jansen, Michał Włodarczyk, Peter Sanders, Grzegorz Herman, Fabrizio Grandoni
2020 European Symposium on Algorithms  
Namely, we prove that Max CSP(Γ) parameterized by the number of variables n is either polynomial-time solvable, or there exists an integer d ≥ 2 depending on Γ, such that: 1) An instance of Max CSP(Γ)  ...  We study the NP-hard cases through the lens of kernelization and provide a complete characterization of Max CSP(Γ) with respect to the optimal compression size.  ...  On the exponential-time front, we have shown that Max d-CNF-SAT is as hard as any Max CSP of degree d as long as negative weights are allowed.  ... 
doi:10.4230/lipics.esa.2020.63 dblp:conf/esa/Jansen020 fatcat:vdmlgng22nebvltgqwmnfgmei4

New Search Heuristics for Max-CSP [chapter]

Kalev Kask
2000 Lecture Notes in Computer Science  
In this paper we extend this work to Max-CSP.  ...  The approach i n volves extracting heuristics from a parameterized approximation scheme called Mini-Bucket elimination that allows controlled trade-o between computation and accuracy.  ...  CSP23 trace of Elim-Max-CSP b A trace of MB-Max-Execution of Elim-Max-CSP and MB- :::; x p be an assignment to the rst p variables in d.  ... 
doi:10.1007/3-540-45349-0_20 fatcat:wqqojwcmlne3vpvgrl374r23z4

Improved Parameterized Algorithms for Constraint Satisfaction [article]

Eun Jung Kim, Ryan Williams
2011 arXiv   pre-print
As a consequence, we obtain O(k)-variable bikernels for boolean CSPs of arity c for every fixed c, and for permutation CSPs of arity 3.  ...  For instance, a simple random assignment for Max-E3-Sat allows 7/8-approximation and for every >0 there is no polynomial-time (7/8+)-approximation unless P=NP.  ...  Acknowledgement The authors would like to thank Daniel Gonçalves for valuable discussion which inspired the results of Section 5.  ... 
arXiv:1008.0213v2 fatcat:ve5r7knodzfabkpoj25mp4e66u

Page 10259 of Mathematical Reviews Vol. , Issue 2004m [page]

2004 Mathematical Reviews  
(English summary) Special issue on parameterized computation and complexity. J. Comput. System Sci. 67 (2003), no. 4, 723-741.  ...  Our approximation algorithm implies that a wide class of 2-CSPs called regular 2-CSPs can all be approximated beyond their random assignment threshold.”  ... 

Optimal polynomial-time compression for Boolean Max CSP [article]

Bart M.P. Jansen, Michał Włodarczyk
2020 arXiv   pre-print
Namely, we prove that Max CSP(Γ) parameterized by the number of variables n is either polynomial-time solvable, or there exists an integer d > 2 depending on Γ, such that 1.  ...  We study the NP hard cases through the lens of kernelization and provide a complete characterization of Max CSP(Γ) with respect to the optimal compression size.  ...  Conclusions and open problems We have provided a complete characterization of the optimal compression for Max CSP(Γ) in the case of a Boolean domain. a natural question arises about larger domains.  ... 
arXiv:2002.03443v1 fatcat:4yag7aw6tncytk4sa3jpbak7de

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.  ...  Finally, we show that the equality constraint over a non-Boolean domain is non-supermodular, and, when combined with some simple unary constraints, gives rise to cases of Max CSP which are hard even to  ...  and unary constraints gives rise to versions of Max CSP that are hard even to approximate.  ... 
doi:10.1007/978-3-540-24749-4_14 fatcat:k2fq6aljyzan3e2hn376u6zley

All Ternary Permutation Constraint Satisfaction Problems Parameterized Above Average Have Kernels with Quadratic Numbers of Variables [article]

Gregory Gutin, Leo van Iersel, Matthias Mnich, Anders Yeo
2011 arXiv   pre-print
We prove that all ternary Permutation-CSPs parameterized above average have kernels with quadratic numbers of variables.  ...  An instance of such a problem consists of a set of variables V and a multiset of constraints, which are ordered triples of distinct variables of V.  ...  A derandomization argument leads to |Πi| 6 -approximation algorithms for the problems Max-Π i -CSP [6] .  ... 
arXiv:1004.1956v3 fatcat:ajf4rip7kbckdmn7yez35prg7q

Every ternary permutation constraint satisfaction problem parameterized above average has a kernel with a quadratic number of variables

Gregory Gutin, Leo van Iersel, Matthias Mnich, Anders Yeo
2012 Journal of computer and system sciences (Print)  
We prove that every ternary Permutation-CSP parameterized above average has a kernel with a quadratic number of variables.  ...  An instance of such a problem consists of a set of variables V and a multiset of constraints, which are ordered triples of distinct variables of V .  ...  A derandomization argument leads to |Π i | 6 -approximation algorithms for the problems Max-Π i -CSP [6] .  ... 
doi:10.1016/j.jcss.2011.01.004 fatcat:5h3tfwpk5neyxk5arljmd7okxe

On the Parameterized Complexity of Clustering Incomplete Data into Subspaces of Small Rank

Robert Ganian, Iyad Kanj, Sebastian Ordyniak, Stefan Szeider
2020 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
We draw a detailed landscape of the complexity and parameterized complexity of the problem with respect to several natural parameters that are desirably small and with respect to several well-studied CSP  ...  We formalize the problem mentioned above and study its classical and parameterized complexity.  ...  Stefan Szeider acknowledges the support of the Austrian Research Funds (FWF), Project P 32441.  ... 
doi:10.1609/aaai.v34i04.5804 fatcat:igkdu27ydzcpjmppd5rrms266i

Parameterized Complexity and Kernelizability of Max Ones and Exact Ones Problems [chapter]

Stefan Kratsch, Dániel Marx, Magnus Wahlström
2010 Lecture Notes in Computer Science  
We study the parameterized complexity of these problems, including the question whether they admit polynomial kernels.  ...  For a finite set Γ of Boolean relations, Max Ones SAT(Γ ) and Exact Ones SAT(Γ ) are generalized satisfiability problems where every constraint relation is from Γ , and the task is to find a satisfying  ...  Recently, there have been investigations of the hardness of CSP from the viewpoint of parameterized complexity [15, 13] .  ... 
doi:10.1007/978-3-642-15155-2_43 fatcat:nuloby4el5agdil6gaq6dtgnhq

Page 8500 of Mathematical Reviews Vol. , Issue 2002K [page]

2002 Mathematical Reviews  
Tight bounds for approximation performance ratios are obtained for every problem in Max Ones, Min CSP, and Min Ones.  ...  In this paper the authors study four classes of constraint satis- faction problems: Max CSP (Min CSP) is the class of problems each of which maximizes the number of satisfied constraints (min- imizes the  ... 
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