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Boolean approximate counting CSPs with weak conservativity, and implications for ferromagnetic two-spin [article]

Miriam Backens, Andrei Bulatov, Leslie Ann Goldberg, Colin McQuillan, Stanislav Živný
2019 arXiv   pre-print
We analyse the complexity of approximate counting constraint satisfactions problems #CSP(F), where F is a set of nonnegative rational-valued functions of Boolean variables.  ...  The resulting classification is employed to characterise the complexity of a wide range of two-spin problems, fully classifying the ferromagnetic case.  ...  Theorem 1 relaxes the conservativity assumption in known counting CSP classifications by adding only two permissive unaries to the set F of constraint functions.  ... 
arXiv:1804.04993v2 fatcat:2ujg5idu2vhxhl76z4yem5swha

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  ...  -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

Model Reductions for Inference: Generality of Pairwise, Binary, and Planar Factor Graphs

Frederik Eaton, Zoubin Ghahramani
2013 Neural Computation  
We investigate the expressive power of three classes of model-those with binary variables, with pairwise factors, and with planar topology-as well as their four intersections.  ...  We formalize a notion of "simple reduction" for the problem of inferring marginal probabilities and consider whether it is possible to "simply reduce" marginal inference from general discrete factor graphs  ...  We also thank Tom Minka, Yee Whye Teh, Jonathan Yedidia, Tom Heskes, Wim Wiegerinck, Alex Ihler, and Dror Weitz for replying to queries, and three anonymous reviewers for thoughtful and useful feedback  ... 
doi:10.1162/neco_a_00441 pmid:23547951 fatcat:at7uw6ftafdbhkr3jzbjgwrypa

The quantum adiabatic algorithm applied to random optimization problems: The quantum spin glass perspective

V. Bapst, L. Foini, F. Krzakala, G. Semerjian, F. Zamponi
2013 Physics reports  
These problems correspond to mean field spin glasses that have been extensively studied in the classical case.  ...  Random optimization problems provide a natural testbed to compare its efficiency with that of classical algorithms.  ...  Biroli Computations were performed in part at the MesoPSL computing center, with support from Région Ile de France and ANR, in part using HPC resources  ... 
doi:10.1016/j.physrep.2012.10.002 fatcat:s6gnhlt3yzf6xpe3rq6uamqsyy

Computational Counting Creative Commons BY 3.0 Unported license

Peter Bürgisser, Leslie Goldberg, Mark Jerrum, Pascal Koiran, Peter Leslie, Ann Goldberg, Mark Jerrum, Pascal License, Peter Bürgisser, Ann Leslie, Mark Goldberg, Pascal Jerrum (+1 others)
A total of 43 researchers from all over the world, with interests and expertise in different aspects of computational counting, actively participated in the meeting.  ...  Dagstuhl Seminar 13031 "Computational Counting" was held from 13th to 18th January 2013, at Schloss Dagstuhl-Leibniz Center for Informatics.  ...  Fast and Slow Mixing in the Ferromagnetic Potts Model On the average number of roots of a real sparse polynomial Geometric Complexity Theory and Counting The complexity of counting CSP with complex  ... 

The computational complexity of approximation of partition functions

Colin McQuillan
of degree-two #CSPs with Boolean relations and weights on variables. -� We classify the complexity of the problem #CSP(F) for arbitrary finite domains when enough non-negative-valued arity 1 functions  ...  of Jerrum and Sinclair to give FPRASes for a large class of degree-two Boolean #CSPs. -� We initiate the classification of degree-two Boolean #CSPs where the constraint language consists of a single arity  ...  The complexity of approximating conservative counting CSPs In Chapter 6 we give a classification for conservative #CSPs with an arbitrary finite domain.  ... 
doi:10.17638/00012893 fatcat:jpzpa3igcjfnhnzuv4qg6kabpy

Dagstuhl Reports, Volume 7, Issue 8, August 2017, Complete Issue [article]

The unique scientific atmosphere and the historic building provided not only all the room we needed for our program and the working groups, but also plenty of opportunities for continued discussions and  ...  We further thank Tamara Mchedlidze for helping us collecting the contributions and preparing this report.  ...  Specifically, given a Boolean constraint language Γ and a degree bound ∆, we study the complexity of #CSP ∆ (Γ), which is the problem of counting satisfying assignments to CSP instances with constraints  ... 
doi:10.4230/dagrep.7.8 fatcat:gksmijgk5ff6reblxsqnt33aze

Dagstuhl Reports, Volume 3, Issue 1, January 2013, Complete Issue [article]

Richerby, "The complexity of approximating conservative counting CSPs," arXiv:1208.1783v2 [cs.CC].  ...  counting weighted matchings or perfect matchings, the subgraphs world problem transformed from the ferromagnetic Ising model, and all counting CSPs and Holant problems with symmetric constraint functions  ...  In our opinion, solutions will bring us to the next level of system creation towards hardware/software co-design, with the benefit of faster time-to-market, improved reuse and conservation of resources  ... 
doi:10.4230/dagrep.3.1 fatcat:tt7daiu6fjhb3i3npxmz5ul2gy

Polarization and Spatial Coupling:Two Techniques to Boost Performance

Seyed Hamed Hassani
CSP models.  ...  We consider simple decimation algorithms (e.g., the unit clause propagation algorithm) for the coupled CSP models and provide a machinery to analyze these algorithms.  ...  Further Remarks In this section we will explain two further (and indirect) implications of Theorems 4.2 and 4.3.  ... 
doi:10.5075/epfl-thesis-5706 fatcat:3tzdhrhfojbinke67vixx53bui

Methods for Inference in Graphical Models

Adrian Weller
We derive new results for this approach, including a general decomposition theorem for models of any order and number of labels, extensions of results for binary pairwise models with submodular cost functions  ...  Next we consider methods of approximate inference, with particular emphasis on the Bethe approximation, which is in widespread use and has proved remarkably effective, yet is still far from being completely  ...  that are aligned with the same spin, where β = 1 kT as in (2.3).  ... 
doi:10.7916/d8jd4vdc fatcat:g7sqtasi7jgclnauxiui5u4yvy

Characterising Structure and Stability of Materials using Machine Learning

Andrea Anelli
I want to express a sincere "Thank you" for having coped with me for all these years.  ...  Among the members of the group, I would like to express my gratitude to Edoardo, Gabriele, Daniele, Venkat and Piero for being my first points of contact with the small world of Lausanne, the science of  ...  Atomic and ferromagnetic molecular structures are shown as empty circles and crosses, respectively.  ... 
doi:10.5075/epfl-thesis-7977 fatcat:ghd6fli43zdppagatliss5fjmu


Caius, Manuela Panoiu, Rob Raluca
The controlling scheme is made in LabVIEW, which permits visualisation of the both input and output of the amplifier and also gain control using parallel port.  ...  VEGA-1/0023/08 "Theoretical apparatus for risk analysis and risk evaluation of transport telematic systems".  ...  Acknowledgement This paper was supported by projects APVV-0176-071/0453/08 and KEGA 3/7426/09. Acknowledgements This paper was supported by the scientific grant agency VEGA, grant No.  ...