@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}
}
@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}
}
