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Complexity and Approximability of Parameterized MAX-CSPs

2017
*
Algorithmica
*

We study the optimization version

doi:10.1007/s00453-017-0310-8
fatcat:ofab3wvgwjg75kehvxwaecmytm
*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 ...##
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Constraint Satisfaction Problems Parameterized Above or Below Tight Bounds: A Survey
[article]

2011
*
arXiv
*
pre-print

We also consider

arXiv:1108.4803v1
fatcat:3wxkx7blgjfkzmqtw4jn7qdlqa
*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. ...##
###
Constraint Satisfaction Problems Parameterized above or below Tight Bounds: A Survey
[chapter]

2012
*
Lecture Notes in Computer Science
*

We also consider

doi:10.1007/978-3-642-30891-8_14
fatcat:r6ztg5kqybefhfxd2myyxtbq6q
*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. ...##
###
Experimental Evaluation of Parameterized Algorithms for Graph Separation Problems: Half-Integral Relaxations and Matroid-based Kernelization
[article]

2018
*
arXiv
*
pre-print

In the recent years we have witnessed a rapid development

arXiv:1811.07779v1
fatcat:w2q6qjlupffujot5op7zkqywey
*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. ...##
###
Optimal Polynomial-Time Compression for Boolean Max CSP

2020
*
European Symposium on Algorithms
*

Namely, we prove that

doi:10.4230/lipics.esa.2020.63
dblp:conf/esa/Jansen020
fatcat:vdmlgng22nebvltgqwmnfgmei4
*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. ...##
###
New Search Heuristics for Max-CSP
[chapter]

2000
*
Lecture Notes in Computer Science
*

In this paper we extend this work to

doi:10.1007/3-540-45349-0_20
fatcat:wqqojwcmlne3vpvgrl374r23z4
*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. ...##
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Improved Parameterized Algorithms for Constraint Satisfaction
[article]

2011
*
arXiv
*
pre-print

As a consequence, we obtain O(k)-variable bikernels for boolean

arXiv:1008.0213v2
fatcat:ve5r7knodzfabkpoj25mp4e66u
*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. ...##
###
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]

2020
*
arXiv
*
pre-print

Namely, we prove that

arXiv:2002.03443v1
fatcat:4yag7aw6tncytk4sa3jpbak7de
*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. ...##
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Identifying Efficiently Solvable Cases of Max CSP
[chapter]

2004
*
Lecture Notes in Computer Science
*

In this paper we study the

doi:10.1007/978-3-540-24749-4_14
fatcat:k2fq6aljyzan3e2hn376u6zley
*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*. ...##
###
All Ternary Permutation Constraint Satisfaction Problems Parameterized Above Average Have Kernels with Quadratic Numbers of Variables
[article]

2011
*
arXiv
*
pre-print

We prove that all ternary Permutation-

arXiv:1004.1956v3
fatcat:ajf4rip7kbckdmn7yez35prg7q
*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] . ...##
###
Every ternary permutation constraint satisfaction problem parameterized above average has a kernel with a quadratic number of variables

2012
*
Journal of computer and system sciences (Print)
*

We prove that every ternary Permutation-

doi:10.1016/j.jcss.2011.01.004
fatcat:5h3tfwpk5neyxk5arljmd7okxe
*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] . ...##
###
On the Parameterized Complexity of Clustering Incomplete Data into Subspaces of Small Rank

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

doi:10.1609/aaai.v34i04.5804
fatcat:igkdu27ydzcpjmppd5rrms266i
*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. ...##
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Parameterized Complexity and Kernelizability of Max Ones and Exact Ones Problems
[chapter]

2010
*
Lecture Notes in Computer Science
*

We study the

doi:10.1007/978-3-642-15155-2_43
fatcat:nuloby4el5agdil6gaq6dtgnhq
*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] . ...##
###
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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