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On LP-based Approximability for Strict CSPs [chapter]

Amit Kumar, Rajsekar Manokaran, Madhur Tulsiani, Nisheeth K. Vishnoi
2011 Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms  
We present a generic linear program (LP) for a large class of strict-CSPs and give a systematic way to convert integrality gaps for this LP into UGC-based inapproximability results.  ...  He noted that his techniques do no apply to CSPs with strict constraints (all of which must be satisfied) such as Vertex Cover. In this paper we address the approximability of these strict-CSPs.  ...  The authors would like to thank Oded Regev for bringing the paper [AKS09] to our notice and also observing that every problem in the class k-strict ↑ -CSP over the alphabet {0, 1} can be reduced to a  ... 
doi:10.1137/1.9781611973082.121 dblp:conf/soda/KumarMTV11 fatcat:b4gslekhejbzfevzaz5ticl3fe

The Constraint Satisfaction Problem: Complexity and Approximability (Dagstuhl Seminar 18231)

Martin Grohe, Venkatesan Guruswami, Stanislav Zivny, Michael Wagner
2018 Dagstuhl Reports  
CSPs constitute a very rich and yet sufficiently manageable class of problems to give a good perspective on general computational phenomena.  ...  For instance, they help to understand which mathematical properties make a computational problem tractable (in a wide sense, e.g., polynomial-time solvable, non-trivially approximable, fixed-parameter  ...  Using our techniques, we also simplify and strengthen the result by Khot et al. [2] on (strong) approximation resistance for LPs.  ... 
doi:10.4230/dagrep.8.6.1 dblp:journals/dagstuhl-reports/GroheGZ18 fatcat:3bqo62ly3rgzlnh3bmkvwbuwea

On the Optimality of a Class of LP-based Algorithms [article]

Amit Kumar, Rajsekar Manokaran, Madhur Tulsiani, Nisheeth K. Vishnoi
2009 arXiv   pre-print
Typically, one can write an LP relaxation and then round the solution. In this paper, we explain why the simple LP-based rounding algorithm for the \\VC problem is optimal assuming the UGC.  ...  Complementing Raghavendra's result, our result generalizes to a class of strict, covering/packing type CSPs.  ...  Acknowledgments The authors would like to thank Oded Regev for bringing the paper [AKS09] to our notice and also observing that every problem in the class k-sm-CSP over the alphabet {0, 1} can be reduced  ... 
arXiv:0912.1776v1 fatcat:snr5f2nqt5ghdnf6bmr7vsuic4

Optimal Constant-Time Approximation Algorithms and (Unconditional) Inapproximability Results for Every Bounded-Degree CSP [article]

Yuichi Yoshida
2010 arXiv   pre-print
Therefore, for every bounded-degree CSP, we give the best constant-time approximation algorithm among all.  ...  Specifically, we present the followings: (i) For every CSP, we construct an oracle that serves an access, in constant time, to a nearly optimal solution to a basic LP relaxation of the CSP.  ...  Acknowledgements The author is grateful to Hiro Ito and Suguru Tamaki for valuable comments on an earlier draft of this paper.  ... 
arXiv:1006.3368v2 fatcat:ttmtf5oatjamrm26dcajm23uou

The Power of the Combined Basic LP and Affine Relaxation for Promise CSPs [article]

Joshua Brakensiek, Venkatesan Guruswami, Marcin Wrochna, Stanislav Živný
2020 arXiv   pre-print
CSPs based on "polymorphisms," operations that map tuples in the strict form of each constraint to tuples in the corresponding weak form.  ...  In a promise CSP, each constraint comes in two forms: "strict" and "weak," and in the associated decision problem one must distinguish between being able to satisfy all the strict constraints versus not  ...  Acknowledgments We thank Libor Barto, Andrei Krokhin, and Jakub Opršal for useful comments and encouragement. We also thank anonymous reviewers for many helpful comments.  ... 
arXiv:1907.04383v3 fatcat:uw43kazqtrcnlnsobu5cg4gvty

Towards a Characterization of Constant-Factor Approximable Min CSPs [chapter]

Víctor Dalmau, Andrei Krokhin, Rajsekar Manokaran
2014 Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms  
of such distributions on polymorphisms of each arity is necessary and sufficient for the finiteness of the integrality gap for the basic LP relaxation of Min CSP(Γ).  ...  A recent result of Ene et al. says that, under the mild technical condition that Γ contains the equality relation, the basic LP relaxation is optimal for constant-factor approximation for Min CSP(Γ) unless  ...  Raghavendra proved [37] that one SDP-based algorithm provides optimal approximation for all problems Max CSP(Γ) assuming the UGC.  ... 
doi:10.1137/1.9781611973730.58 dblp:conf/soda/DalmauKM15 fatcat:f5ko7uozzbaorctfoa32yrbgiu

Towards a characterization of constant-factor approximable finite-valued CSPs

Víctor Dalmau, Andrei Krokhin, Rajsekar Manokaran
2018 Journal of computer and system sciences (Print)  
Raghavendra proved [17] that one SDP-based algorithm provides optimal approximation for all problems GCSP(Γ) assuming the UGC.  ...  Ene et al. have shown that, under a mild technical condition, the basic LP relaxation is optimal for constant-factor approximation for VCSP(Γ) unless the Unique Games Conjecture fails.  ...  We conjecture that Min CSP(Γ) is constant-factor approximable for all such languages, even 20 without the assumption on eq A .  ... 
doi:10.1016/j.jcss.2018.03.003 fatcat:hnmmumxwevffplybvkxme5e7g4

Approximation schemes via Sherali-Adams hierarchy for dense constraint satisfaction problems and assignment problems

Yuichi Yoshida, Yuan Zhou
2014 Proceedings of the 5th conference on Innovations in theoretical computer science - ITCS '14  
In this paper, we give a unified method of showing these approximation schemes based on the Sherali-Adams linear programming relaxation hierarchy.  ...  We consider approximation schemes for the maximum constraint satisfaction problems and the maximum assignment problems.  ...  Assuming the Unique Games Conjecture, a canonical LP relaxation (also referred to as the Basic LP ) is shown to provide optimal approximation guarantee for CSPs with strict constraints [10] .  ... 
doi:10.1145/2554797.2554836 dblp:conf/innovations/YoshidaZ14 fatcat:s5jn2jbg7bdqznmyt6vybzatda

The limits of SDP relaxations for general-valued CSPs

Johan Thapper, Stanislav Zivny
2017 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)  
For Γ corresponding to linear equations in an Abelian group, this result follows from existing work on inapproximability of Max-CSPs.  ...  Our results hold for general-valued constraint languages, i.e., sets of functions on a fixed finite domain that take on rational or infinite values, and thus also hold in notable special cases of {0, ∞  ...  relaxations and approximability of CSPs [51] .  ... 
doi:10.1109/lics.2017.8005087 dblp:conf/lics/ThapperZ17 fatcat:3n5i4goiwnclflpkx5dmmkox6e

Interprovincial spoke-to-hub transport using the Impella Recover LP 5.0 left ventricular assist device as a bridge to long-term circulatory support

Mina Guirgis, Kanwal Kumar, Shelley Zieroth, Roger Philipp, Alan H. Menkis, Darren H. Freed
2010 Canadian Journal of Cardiology  
Based on a literature review, we report the first case demonstrating successful use of the Impella Recover LP 5.0 LVAD, implanted under local anesthetic, for the purpose of interprovincial spoke-to-hub  ...  Based on a review of the literature, the present report describes the first case demonstrating successful use of the Impella Recover LP 5.0 LVAD, implanted under local anesthetic, for the purposes of interprovincial  ...  Based on a literature review, we report the first case demonstrating successful use of the Impella Recover LP 5.0 LVAD, implanted under local anesthetic, for the purpose of interprovincial spoke-to-hub  ... 
doi:10.1016/s0828-282x(10)70443-8 pmid:20931101 pmcid:PMC2954541 fatcat:y65tdechw5eh3pvtgehomdspza

The Power of the Combined Basic Linear Programming and Affine Relaxation for Promise Constraint Satisfaction Problems

Joshua Brakensiek, Venkatesan Guruswami, Marcin Wrochna, Stanislav Živný
2020 SIAM journal on computing (Print)  
algebraic approach to promise CSPs based on"polymorphisms,"" operations that map tuples in the strict form of each constraint to tuples in the corresponding weak form.  ...  This work concerns the theme of designing algorithms for PCSPs based on a rich enough family of polymorphisms.  ...  We thank Libor Barto, Andrei Krokhin, and Jakub Opr\v sal for useful comments and encouragement. We also thank anonymous reviewers for many helpful comments.  ... 
doi:10.1137/20m1312745 fatcat:hd7moxv3crbkbeulczbttxv7am

Towards a Characterization of Constant-Factor Approximable Finite-Valued CSPs [article]

Victor Dalmau, Andrei Krokhin, Rajsekar Manokaran
2018 arXiv   pre-print
Using the algebraic approach to the CSP, we give new natural algebraic conditions for the finiteness of the integrality gap for the basic LP relaxation of VCSP(Γ).  ...  A recent result of Ene et al. says that, under the mild technical condition that Γ contains the equality relation, the basic LP relaxation is optimal for constant-factor approximation for VCSP(Γ) unless  ...  The authors would like to thank Per Austrin, Johan Håstad, and Venkatesan Guruswami for useful discussions. We would also like to thank the anonymous referees for useful comments.  ... 
arXiv:1610.01019v2 fatcat:7mkusvcxwbd4lcxblocqyamy7q

Exact and Approximation Algorithms for the Maximum Constraint Satisfaction Problem over the Point Algebra

Yoichi Iwata, Yuichi Yoshida, Marc Herbstritt
2013 Symposium on Theoretical Aspects of Computer Science  
As for approximation, we give a 0.4586-approximation algorithm when the objective is maximizing the number of satisfied constraints, and give an O(log n log log n)-approximation algorithm when the objective  ...  Acknowledgments The authors are grateful to François Le Gall for valuable discussions about the usage of sparse matrix product for the exact algorithm.  ...  Then, we obtain an O(log n log log n)-approximation algorithm for the symmetric multicut problem. 2 O * (·) hides a factor polynomial in n. 3 We denote by log the logarithm to the base 2.  ... 
doi:10.4230/lipics.stacs.2013.127 dblp:conf/stacs/IwataY13 fatcat:ssd4orheqfcxhhusa5usp5xi3i

Impact of lipopolysaccharide-induced acute inflammation on baroreflex-controlled sympathetic arterial pressure regulation

Takeshi Tohyama, Keita Saku, Toru Kawada, Takuya Kishi, Keimei Yoshida, Takuya Nishikawa, Hiroshi Mannoji, Kazuhiro Kamada, Kenji Sunagawa, Hiroyuki Tsutsui, Michael Bader
2018 PLoS ONE  
We investigated the impact of LPS-induced acute inflammation on SNA and AP regulation by performing baroreflex open-loop analysis. Methods Ten anesthetized Sprague-Dawley rats were used.  ...  We matched CSP to AP to establish the baroreflex closed-loop condition, whereas we decoupled CSP from AP to establish the baroreflex open-loop condition and changed CSP stepwise to evaluate the baroreflex  ...  Takako Takehara and the staff of the Department of Cardiovascular Medicine, Kyushu University for technical support. Author Contributions  ... 
doi:10.1371/journal.pone.0190830 pmid:29329321 pmcid:PMC5766102 fatcat:j774lr4hezc7rfglnfdekguhbq

Zero-Temperature Limit of a Convergent Algorithm to Minimize the Bethe Free Energy [article]

Tomas Werner
2011 arXiv   pre-print
Under certain conditions, the algorithm combines the complementary advantages of the max-product belief propagation and max-sum diffusion (LP relaxation): it yields good approximation of both ground states  ...  These algorithms were formulated only for non-zero temperature (thus finding fixed points of the sum-product algorithm) and their possible extension to zero temperature is not obvious.  ...  The author thanks Alexander Shekhovtsov for discussions.  ... 
arXiv:1112.5298v1 fatcat:cawy52be3jhm5j3eex42e52hly
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