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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
In the field of constraint satisfaction problems (CSP), promise CSPs are an exciting new direction of study.  ...  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  ...  A From Relaxations to Minion Homomorphisms In this appendix, we recall the definition of the minion Q conv and prove Lemma 7 from Section 5.  ... 
arXiv:1907.04383v3 fatcat:uw43kazqtrcnlnsobu5cg4gvty

An Algorithmic Blend of LPs and Ring Equations for Promise CSPs [article]

Joshua Brakensiek, Venkatesan Guruswami
2018 arXiv   pre-print
Promise CSPs are a relaxation of constraint satisfaction problems where the goal is to find an assignment satisfying a relaxed version of the constraints.  ...  We also abstract a framework based on reducing a promise CSP to a CSP over an infinite domain, solving it there, and then rounding the solution to an assignment for the promise CSP instance.  ...  The authors also thank Libor Barto, Andrei Krokhin and Jakub Opršal for a myriad of helpful comments on this paper at Dagstuhl Seminar 18231 on "The Constraint Satisfaction Problem: Complexity and Approximability  ... 
arXiv:1807.05194v1 fatcat:wptigingdref3kv6oasx5xtmce

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)  
Building on the impetus of [1], Brakensiek and Guruswami systematically studied PCSPs under the polymorphic lens and established promising links to the universal-algebraic framework developed for CSPs  ...  This concerns a vast generalization of the CSP framework to the class of promise CSPs (PCSPs). In a PCSP, each constraint comes in two forms:"strict"" and"weak.""  ...  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

The combined basic LP and affine IP relaxation for promise VCSPs on infinite domains [article]

Caterina Viola, Stanislav Zivny
2021 arXiv   pre-print
In this work, we extend an existing tractability result to the three generalisations of CSPs combined: We give a sufficient condition for the combined basic linear programming and affine integer programming  ...  relaxation for exact solvability of promise valued CSPs over infinite-domains.  ...  The power of the combined relaxation for (finite-domain) promise CSPs was established in [20] .  ... 
arXiv:2007.01779v2 fatcat:jiweubnh35clngysvhyi3azjhu

Logic-Based Solution Methods for Optimal Control of Hybrid Systems

A. Bemporad, N. Giorgetti
2006 IEEE Transactions on Automatic Control  
The resulting "hybrid" solver proposed here takes advantage of CSP solvers for dealing with satisfiability of logic constraints very efficiently.  ...  We propose a suitable model of the hybrid dynamics and a class of optimal control problems that embrace both symbolic and continuous variables/functions, and that are tailored to the use of the new hybrid  ...  The basic ingredients for an integrated approach of MIP and CLP are 1) a linear program (LP) obtained by relaxing a mixed integer linear programming (MILP) problem and 2) a CLP feasibility problem.  ... 
doi:10.1109/tac.2006.876949 fatcat:5s63fkonfncizlvmylystmrx5e

On the Power of Symmetric LP and SDP Relaxations

James R. Lee, Prasad Raghavendra, David Steurer, Ning Tan
2014 2014 IEEE 29th Conference on Computational Complexity (CCC)  
We study the computational power of general symmetric relaxations for combinatorial optimization problems, both in the linear programming (LP) and semidefinite programming (SDP) case.  ...  This result gives the first lower bounds for symmetric SDP relaxations of Max CSPs, and indicates that the sum-of-squares method provides the "right" SDP relaxation for this class of problems.  ...  Prasad Raghavendra and Ning Tan acknowledge support from an NSF Career Award and an Alfred P. Sloan Research Fellowship. David Steurer's research is supported by an NSF Career Award and an Alfred P.  ... 
doi:10.1109/ccc.2014.10 dblp:conf/coco/LeeRST14 fatcat:rljvsqsehvfmvnnjoz6wrtidhq

Algebraic approach to promise constraint satisfaction [article]

Libor Barto, Jakub Bulín, Andrei Krokhin, Jakub Opršal
2019 arXiv   pre-print
A new version of the CSP, the promise CSP (PCSP) has recently been proposed, motivated by open questions about the approximability of variants of satisfiability and graph colouring.  ...  The complexity and approximability of the constraint satisfaction problem (CSP) has been actively studied over the last 20 years.  ...  Acknowledgements We would like to thank Libor Barto, Mirek Olšák, Alex Kazda, Josh Brakensiek, Venkat Guruswami, Erkko Lehtonen, and Marcello Mamino for valuable discussions.  ... 
arXiv:1811.00970v3 fatcat:r2pgvc74ffcxzec6fqdkwvznm4

No Small Linear Program Approximates Vertex Cover within a Factor 2 - ϵ [article]

Abbas Bazzi, Samuel Fiorini, Sebastian Pokutta, Ola Svensson
2015 arXiv   pre-print
We prove the following unconditional result about linear programming (LP) relaxations of the problem: every LP relaxation that approximates vertex cover within a factor 2-ϵ has super-polynomially many  ...  The vertex cover problem is one of the most important and intensively studied combinatorial optimization problems.  ...  Research was partially conducted at the Oberwolfach Workshop 1446 and Dagstuhl Workshop 15082.  ... 
arXiv:1503.00753v2 fatcat:bwfcdxrqavbink3wcdwucz3xsy

CLAP: A New Algorithm for Promise CSPs [article]

Lorenzo Ciardo, Stanislav Živný
2022 arXiv   pre-print
We propose a new algorithm for Promise Constraint Satisfaction Problems (PCSPs). It is a combination of the Constraint Basic LP relaxation and the Affine IP relaxation (CLAP).  ...  We give a characterisation of the power of CLAP in terms of a minion homomorphism.  ...  A different relaxation of PCSPs is the basic affine integer programming relaxation (AIP) [19] .  ... 
arXiv:2107.05018v2 fatcat:254pl4pog5aybpomgcb4xylusm

Bridging between 0/1 and Linear Programming via Random Walks [article]

Joshua Brakensiek, Venkatesan Guruswami
2019 arXiv   pre-print
starting distribution, and a time varying distribution for the evolution of the random walk that is itself computed via an LP at each step (a solution to which is guaranteed based on the minimax theorem  ...  If the domain of the variables is relaxed to [0,1], the associated linear program can of course be solved in polynomial time.  ...  Acknowledgments We thank Brian Axelrod, Dima Kogan and anonymous reviewers for helpful feedback on the manuscript.  ... 
arXiv:1904.04860v1 fatcat:mru5bc6lhnh5tjn2sfyxoyhuqe

Chapter 4 Constraint Programming [chapter]

Francesca Rossi, Peter van Beek, Toby Walsh
2008 Foundations of Artificial Intelligence  
Walsh 183 for finding solutions to CSPs that maintain a level of local consistency during the search (e.g., [30, 54, 68] ).  ...  The basic idea in constraint programming is that the user states the constraints and a general purpose constraint solver is used to solve them.  ...  Linear relaxations have been proposed for a number of global constraints including the all different, circuit and cumulative constraints [72] . Such relaxations can then be given to a LP solver.  ... 
doi:10.1016/s1574-6526(07)03004-0 fatcat:vrrxlx2nhjaajj27uvoepcefqa

CSPs with Global Modular Constraints: Algorithms and Hardness via Polynomial Representations [article]

Joshua Brakensiek, Sivakanth Gopi, Venkatesan Guruswami
2019 arXiv   pre-print
We study the complexity of Boolean constraint satisfaction problems (CSPs) when the assignment must have Hamming weight in some congruence class modulo M, for various choices of the modulus M.  ...  Due to the known classification of tractable Boolean CSPs, this mainly reduces to the study of three cases: 2-SAT, HORN-SAT, and LIN-2 (linear equations mod 2).  ...  We can write the dual of the LP (1) as follows: max i∈[n] p i p i 0 ∀S ∈ F i∈S p i 1 (2) By LP duality the optimum value of the LP (2) is also L and is achieved for some p * 1 , p * 2 , . . . , p * n .  ... 
arXiv:1902.04740v1 fatcat:xv7eh5ybgjezfiimqsdmpr2g4q

Learning-Assisted Automated Planning: Looking Back, Taking Stock, Going Forward

Terry Zimmerman, Subbarao Kambhampati
2003 The AI Magazine  
We extend the survey analysis to suggest promising avenues for future research in learning based on both previous experience and current needs in the planning community.  ...  This article reports on an extensive survey and analysis of research work related to machine learning as it applies to automated planning over the past 30 years.  ...  separate versions of figure 4 for each combination.  ... 
doi:10.1609/aimag.v24i2.1705 dblp:journals/aim/ZimmermanK03 fatcat:5umdmeki4zdlznah2hhdrjpe5e

Computational protein design as an optimization problem

David Allouche, Isabelle André, Sophie Barbe, Jessica Davies, Simon de Givry, George Katsirelos, Barry O'Sullivan, Steve Prestwich, Thomas Schiex, Seydou Traoré
2014 Artificial Intelligence  
The CPD problem is a specific form of binary Cost Function Network (CFN, aka Weighted CSP).  ...  The three-dimensional shape of a protein and its amino acid composition define its biological function. Over millions of years, living organisms have evolved a large catalog of proteins.  ...  We thank the Computing Center of Region Midi-Pyrénées (CALMIP, Toulouse, France) and the GenoToul Bioinformatics Platform of INRA-Toulouse for providing computing resources and support.  ... 
doi:10.1016/j.artint.2014.03.005 fatcat:k7o7nvjc4bbkbk6d4qojshbztu

Limitations of Semidefinite Programs for Separable States and Entangled Games

Aram W. Harrow, Anand Natarajan, Xiaodi Wu
2019 Communications in Mathematical Physics  
were known: the set of separable (i.e. unentangled) states, or equivalently, the 2 → 4 norm of a matrix, and the set of quantum correlations; i.e. conditional probability distributions achievable with  ...  Our unconditional results achieve the same parameters as all of these previous results (for separable states) or as some of the previous results (for quantum correlations).  ...  Acknowledgement AWH and AN were funded by NSF grant CCF-1629809 and AWH was funded by NSF grant CCF-1452616. XW was funded by the NSF Waterman Award of Scott Aaronson.  ... 
doi:10.1007/s00220-019-03382-y fatcat:am5kaeuernh6fgnw7azgwsn3wa
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