@article {Shekhovtsov2018,
	title = {Maximum Persistency via Iterative Relaxed Inference in Graphical Models},
	journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
	volume = {40},
	number = {7},
	year = {2018},
	pages = {1668{\textendash}1682},
	abstract = {We consider the NP-hard problem of MAP-inference for undirected discrete graphical models. We propose a polynomial time and practically efficient algorithm for finding a part of its optimal solution. Specifically, our algorithm marks some labels of the considered graphical model either as (i) optimal, meaning that they belong to all optimal solutions of the inference problem; (ii) non-optimal if they provably do not belong to any solution. With access to an exact solver of a linear programming relaxation to the MAP-inference problem, our algorithm marks the maximal possible (in a specified sense) number of labels. We also present a version of the algorithm, which has access to a suboptimal dual solver only and still can ensure the (non-)optimality for the marked labels, although the overall number of the marked labels may decrease. We propose an efficient implementation, which runs in time comparable to a single run of a suboptimal dual solver. Our method is well-scalable and shows state-of-the-art results on computational benchmarks from machine learning and computer vision.},
	keywords = {discrete optimization, energy minimization, graphical models, LP relaxation, partial optimality, persistency, WCSP},
	issn = {01628828},
	doi = {10.1109/TPAMI.2017.2730884},
	url = {http://www.icg.tugraz.at/},
	author = {Shekhovtsov, Alexander and Swoboda, Paul and Savchynskyy, Bogdan}
}
@conference {Tourani2018,
	title = {MPLP++: Fast, Parallel Dual Block-Coordinate Ascent for Dense Graphical Models},
	booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
	volume = {11208 LNCS},
	year = {2018},
	pages = {264{\textendash}281},
	abstract = {Dense, discrete Graphical Models with pairwise potentials are a powerful class of models which are employed in state-of-the-art computer vision and bio-imaging applications. This work introduces a new MAP-solver, based on the popular Dual Block-Coordinate Ascent principle. Surprisingly, by making a small change to a low-performing solver, the Max Product Linear Programming (MPLP) algorithm [7], we derive the new solver MPLP++ that significantly outperforms all existing solvers by a large margin, including the state-of-the-art solver Tree-Reweighted Sequential (TRW-S) message-passing algorithm [17]. Additionally, our solver is highly parallel, in contrast to TRW-S, which gives a further boost in performance with the proposed GPU and multi-thread CPU implementations. We verify the superiority of our algorithm on dense problems from publicly available benchmarks as well as a new benchmark for 6D Object Pose estimation. We also provide an ablation study with respect to graph density.},
	keywords = {Block-Coordinate-Ascent, graphical models, Message passing algorithms},
	isbn = {9783030012243},
	issn = {16113349},
	doi = {10.1007/978-3-030-01225-0_16},
	author = {Tourani, Siddharth and Shekhovtsov, Alexander and Carsten Rother and Savchynskyy, Bogdan}
}
@article {Kappes2016,
	title = {Multicuts and Perturb \& MAP for Probabilistic Graph Clustering},
	journal = {Journal of Mathematical Imaging and Vision},
	volume = {56},
	number = {2},
	year = {2016},
	month = {jan},
	pages = {221{\textendash}237},
	abstract = {We present a probabilistic graphical model formulation for the graph clustering problem. This enables us to locally represent uncertainty of image partitions by approximate marginal distributions in a mathematically substantiated way, and to rectify local data term cues so as to close contours and to obtain valid partitions. We exploit recent progress on globally optimal MAP inference by integer programming and on perturbation-based approximations of the log-partition function, in order to sample clusterings and to estimate marginal distributions of node-pairs both more accurately and more efficiently than state-of-the-art methods. Our approach works for any graphically represented problem instance. This is demonstrated for image segmentation and social network cluster analysis. Our mathematical ansatz should be relevant also for other combinatorial problems.},
	keywords = {Correlation clustering, graphical models, Multicut, Perturb and MAP},
	issn = {15737683},
	doi = {10.1007/s10851-016-0659-3},
	url = {http://arxiv.org/abs/1601.02088},
	author = {Kappes, Jorg Hendrik and Swoboda, Paul and Savchynskyy, Bogdan and Hazan, Tamir and Christoph Schn{\"o}rr}
}
