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@ARTICLE{4204160, 
author={T. Werner}, 
journal={IEEE Transactions on Pattern Analysis and Machine Intelligence}, 
title={A Linear Programming Approach to Max-Sum Problem: A Review}, 
year={2007}, 
volume={29}, 
number={7}, 
pages={1165-1179}, 
keywords={computational complexity;linear programming;trees (mathematics);NP-hard optimization problem;linear programming;max-sum labeling problem;tree-reweighted max-product;Books;Computer Society;Image analysis;Labeling;Linear programming;Markov random fields;Noise generators;Pattern recognition;Testing;Upper bound;Markov random fields;belief propagation;constraint satisfaction;linear programming relaxation;max-plus;max-product;max-sum;supermodular optimization.;undirected graphical models;Algorithms;Artificial Intelligence;Game Theory;Image Enhancement;Image Interpretation, Computer-Assisted;Imaging, Three-Dimensional;Pattern Recognition, Automated;Programming, Linear}, 
doi={10.1109/TPAMI.2007.1036}, 
ISSN={0162-8828}, 
month={July},}

@ARTICLE{research_report, 
author={T. Werner}, 
journal={Research Reports of CMP}, 
title={A Linear Programming Approach to Max-Sum Problem: A Review}, 
year={2005},
month={December},}

@ARTICLE{2017arXiv170904989W,
   author = {{Werner}, T.},
    title = "{On Coordinate Minimization of Convex Piecewise-Affine Functions}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1709.04989},
 primaryClass = "math.OC",
 keywords = {Mathematics - Optimization and Control, Computer Science - Computer Vision and Pattern Recognition},
     year = 2017,
    month = sep,
   adsurl = {http://adsabs.harvard.edu/abs/2017arXiv170904989W},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@InProceedings{CSP_paper,
author="Apt, Krzysztof R.",
editor="Jaffar, Joxan",
title="The Rough Guide to Constraint Propagation",
booktitle="Principles and Practice of Constraint Programming -- CP'99",
year="1999",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="1--23",
abstract="We provide here a simple, yet very general framework that allows us to explain several constraint propagation algorithms in a systematic way. In particular, using the notions commutativity and semi-commutativity, we show how the well-known AC-3, PC-2, DAC and DPC algorithms are instances of a single generic algorithm. The work reported here extends and simplifies that of Apt [1].",
isbn="978-3-540-48085-3"
}

@article{prusa2004,
  title={Two-dimensional languages},
  author={Pr{\r u}{\v{s}}a, D},
  journal={Faculty of Mathematics and Physics, Charles University in Prague},
  year={2004}
}

@misc{gurobi,
   author = "Gurobi Optimization, Inc.",
   title = "Gurobi Optimizer Reference Manual",
   year = 2016,
   url = "http://www.gurobi.com"
 }

@inproceedings{Komodakis07,
  author    = {Nikos Komodakis and Nikos Paragios and Georgios Tziritas},
  title     = {{MRF} Optimization via Dual Decomposition: Message-Passing Revisited},
  booktitle = {Intl. Conf. on Computer Vision},
  year      = {2007},
}

@Article{schl76,
    Author = {Y.K. {Koval'} and M.I. {Schlesinger}},
    Title = {{Two-dimensional programming in image-analysis problems.}},
    FJournal = {{Automation and Remote Control}},
    Journal = {{Autom. Remote Control}},
    ISSN = {0005-1179; 1608-3032/e},
    Volume = {37},
    Pages = {1269--1285},
    Year = {1976},
    Publisher = {Springer US, New York, NY; Pleiades Publishing, New York, NY; MAIK ``Nauka/Interperiodica'', Moscow},
    Language = {English},
    MSC2010 = {68T10 68T05 68W99 68Q45},
    Zbl = {0389.68048}
}

@article{edmonds1972theoretical,
  title={Theoretical improvements in algorithmic efficiency for network flow problems},
  author={Edmonds, Jack and Karp, Richard M},
  journal={Journal of the ACM (JACM)},
  volume={19},
  number={2},
  pages={248--264},
  year={1972},
  publisher={ACM}
}

@techreport{ford1955simple,
  title={A simple algorithm for finding maximal network flows and an application to the Hitchcock problem},
  author={Ford Jr, Lester R and Fulkerson, Delbert R},
  year={1955},
  institution={RAND CORP SANTA MONICA CA}
}

@inproceedings{juan2007capacity,
  title={Capacity scaling for graph cuts in vision},
  author={Juan, Olivier and Boykov, Yuri},
  booktitle={Computer Vision, 2007. ICCV 2007. IEEE 11th International Conference on},
  pages={1--8},
  year={2007},
  organization={IEEE}
}

@article{ahuja1995capacity,
  title={A capacity scaling algorithm for the constrained maximum flow problem},
  author={Ahuja, Ravindra K and Orlin, James B},
  journal={Networks},
  volume={25},
  number={2},
  pages={89--98},
  year={1995},
  publisher={Wiley Online Library}
}

@inproceedings{Kappes-study-2013,
    author      = {Kappes, J{\"o}rg H. and Andres, Bjoern and Hamprecht, Fred A. and Schn{\"o}rr, Christoph and Nowozin, Sebastian and Batra, Dhruv and Kim, Sungwoong and Kausler, Bernhard X. and Lellmann, Jan and Komodakis, Nikos and Rother, Carsten},
    title       = {A Comparative Study of Modern Inference Techniques for Discrete Energy Minimization Problem},
    booktitle   = {Conf. Computer Vision and Pattern Recognition},
    year        = {2013},
}

@Unpublished{Kovalevsky-diffusion,
  author =       {V. A. Kovalevsky and V. K. Koval},
  title =        {A diffusion algorithm for decreasing the energy of the max-sum labeling problem},
  year =      {approx.\ 1975},
  note = {{Glushkov Institute of Cybernetics, Kiev, USSR. Unpublished}},
}

@article{kolmogorov2006convergent,
  title={Convergent tree-reweighted message passing for energy minimization},
  author={Kolmogorov, Vladimir},
  journal={IEEE transactions on pattern analysis and machine intelligence},
  volume={28},
  number={10},
  pages={1568--1583},
  year={2006},
  publisher={IEEE}
}

@article{schlesinger2007solving,
  title={Solving (max,+) problems of structural pattern recognition using equivalent transformations},
  author={Schlesinger, Michail I and Giginjak, VV},
  journal={Upravlyayushchie Sistemy i Mashiny (Control Systems and Machines), Kiev, Naukova Dumka},
  volume={1},
  year={2007}
}

@article{weiss2012map,
  title={MAP estimation, linear programming and belief propagation with convex free energies},
  author={Weiss, Yair and Yanover, Chen and Meltzer, Talya},
  journal={arXiv preprint arXiv:1206.5286},
  year={2012}
}

@article{johnson2007lagrangian,
  title={Lagrangian relaxation for MAP estimation in graphical models},
  author={Johnson, Jason K and Malioutov, Dmitry M and Willsky, Alan S},
  journal={arXiv preprint arXiv:0710.0013},
  year={2007}
}

@inproceedings{ravikumar2008message,
  title={Message-passing for graph-structured linear programs: Proximal projections, convergence and rounding schemes},
  author={Ravikumar, Pradeep and Agarwal, Alekh and Wainwright, Martin J},
  booktitle={Proceedings of the 25th international conference on Machine learning},
  pages={800--807},
  year={2008},
  organization={ACM}
}

@incollection{bessiere2006constraint,
  title={Constraint propagation},
  author={Bessiere, Christian},
  booktitle={Foundations of Artificial Intelligence},
  volume={2},
  pages={29--83},
  year={2006},
  publisher={Elsevier}
}

@inproceedings{pruuvsa2017lp,
  title={LP relaxations of some NP-hard problems are as hard as any LP},
  author={Pr{\r u}{\v{s}}a, Daniel and Werner, Tomas},
  booktitle={Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms},
  pages={1372--1382},
  year={2017},
  organization={SIAM}
}

@article{boyd2003subgradient,
  title={Subgradient methods},
  author={Boyd, Stephen and Xiao, Lin and Mutapcic, Almir},
  year={2003}
}

@article{cooper2010soft,
  title={Soft arc consistency revisited},
  author={Cooper, Martin C and De Givry, Simon and S{\'a}nchez, Mart{\i} and Schiex, Thomas and Zytnicki, Matthias and Werner, Tom{\'a}{\v{s}}},
  journal={Artificial Intelligence},
  volume={174},
  number={7-8},
  pages={449--478},
  year={2010},
  publisher={Elsevier}
}

@article{kolmogorov2005primal,
  title={Primal-dual algorithm for convex Markov random fields},
  author={Kolmogorov, Vladimir},
  journal={Microsoft Research MSR-TR-2005-117},
  year={2005}
}

@inproceedings{NguyenGSB14,
  author    = {Hiep Nguyen and
               Simon de Givry and
               Thomas Schiex and
               Christian Bessiere},
  title     = {Maintaining Virtual Arc Consistency Dynamically during Search},
  booktitle = {Intl. Conf. on Tools with Artificial Intelligence (ICTAI)},
  pages     = {8--15},
  publisher = {{IEEE} Computer Society},
  year      = {2014},
}


@string{PAMI = "{PAMI}: Transactions on Pattern Analysis and Machine Intelligence"}

@ARTICLE{shekhovtsov-17-persistency,
author={A. Shekhovtsov and P. Swoboda and B. Savchynskyy}, 
journal=PAMI, 
title={Maximum Persistency via Iterative Relaxed Inference with Graphical Models}, 
year={2017}, 
volume={PP}, 
number={99}, 
xpages={1-1}, 
keywords={Computer vision;Graphical models;Inference algorithms;Labeling;Linear programming;Optimization;Signal processing algorithms;LP relaxation;Persistency;WCSP;discrete optimization;energy minimization;graphical models;partial optimality}, 
doi={10.1109/TPAMI.2017.2730884}, 
ISSN={0162-8828}, 
month={July},}

@article{schlesinger1976syntactic,
  title={Syntactic analysis of two-dimensional visual signals in the presence of noise},
  author={Schlesinger, MI},
  journal={Cybernetics},
  volume={12},
  number={4},
  pages={612--628},
  year={1976},
  publisher={Springer}
}

@ARTICLE{Prusa-PAMI-2015,
author={Pr{\r u}{\v s}a, Daniel and Werner, Tom{\'a}{\v s}},
journal={IEEE Trans.\ on Pattern Analysis and Machine Intelligence},
title={Universality of the Local Marginal Polytope},
year={2015},
month={April},
volume={37},
number={4},
pages={898-904},
}