@proceedings {Haller2020,
	title = {A Primal-Dual Solver for Large-Scale Tracking-by-Assignment},
	year = {2020},
	abstract = {We propose a fast approximate solver for the combinatorial problem known as tracking-by-assignment, which we apply to cell tracking. The latter plays a key role in discovery in many life sciences, especially in cell and developmental biology. So far, in the most general setting this problem was addressed by off-the-shelf solvers like Gurobi, whose run time and memory requirements rapidly grow with the size of the input. In contrast, for our method this growth is nearly linear. Our contribution consists of a new (1) de-composable compact representation of the problem; (2) dual block-coordinate ascent method for optimizing the decomposition-based dual; and (3) primal heuristics that reconstructs a feasible integer solution based on the dual information. Compared to solving the problem with Gurobi, we observe an up to 60 times speed-up, while reducing the memory footprint significantly. We demonstrate the efficacy of our method on real-world tracking problems.},
	author = {Stefan Haller and Prakash, Mangal and Hutschenreiter, Lisa and Pietzsch, Tobias and Carsten Rother and Jug, Florian and Swoboda, Paul and Savchynskyy, Bogdan}
}
@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}
}
@article {Swoboda2016,
	title = {Partial Optimality by Pruning for MAP-Inference with General Graphical Models},
	journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
	volume = {38},
	number = {7},
	year = {2016},
	month = {jul},
	pages = {1370{\textendash}1382},
	publisher = {IEEE Computer Society},
	abstract = {We consider the energy minimization problem for undirected graphical models, also known as MAP-inference problem for Markov random fields which is NP-hard in general. We propose a novel polynomial time algorithm to obtain a part of its optimal non-relaxed integral solution. Our algorithm is initialized with variables taking integral values in the solution of a convex relaxation of the MAP-inference problem and iteratively prunes those, which do not satisfy our criterion for partial optimality. We show that our pruning strategy is in a certain sense theoretically optimal. Also empirically our method outperforms previous approaches in terms of the number of persistently labelled variables. The method is very general, as it is applicable to models with arbitrary factors of an arbitrary order and can employ any solver for the considered relaxed problem. Our method{\textquoteright}s runtime is determined by the runtime of the convex relaxation solver for the MAP-inference problem.},
	keywords = {energy minimization, Local polytope, MAP-inference, Markov random fields, partial optimality, persistency},
	issn = {01628828},
	doi = {10.1109/TPAMI.2015.2484327},
	author = {Swoboda, Paul and Shekhovtsov, Alexander and Kappes, Jorg Hendrik and Christoph Schn{\"o}rr and Savchynskyy, Bogdan}
}
@conference {Kappes2015c,
	title = {Probabilistic correlation clustering and image partitioning using perturbed Multicuts},
	booktitle = {Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)},
	volume = {9087},
	year = {2015},
	pages = {231{\textendash}242},
	abstract = {We exploit recent progress on globally optimal MAP inference by integer programming and perturbation-based approximations of the log-partition function. This enables 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. Our approach works for any graphically represented problem instance of correlation clustering, which is demonstrated by an additional social network example.},
	keywords = {Correlation clustering, Multicut, Perturb and MAP},
	isbn = {9783319184609},
	issn = {16113349},
	doi = {10.1007/978-3-319-18461-6_19},
	author = {Kappes, Jorg Hendrik and Swoboda, Paul and Savchynskyy, Bogdan and Hazan, Tamir and Christoph Schn{\"o}rr}
}
@conference {Swoboda-2014,
	title = {Partial Optimality by Pruning for MAP-inference with General Graphical Models},
	booktitle = {IEEE Conference on Computer Vision and Pattern Recognition 2014},
	year = {2014},
	author = {Swoboda, Paul and Savchynskyy, Bogdan and J{\"o}rg H. Kappes and Christoph Schn{\"o}rr}
}
@conference {Swoboda-2014,
	title = {Partial Optimality by Pruning for MAP-inference with General Graphical Models},
	booktitle = {IEEE Conference on Computer Vision and Pattern Recognition 2014},
	year = {2014},
	author = {Swoboda, Paul and Savchynskyy, Bogdan and Kappes, J{\"o}rg H. and Christoph Schn{\"o}rr}
}
@conference {SavchynskyyNIPS2013,
	title = {Global MAP-Optimality by Shrinking the Combinatorial Search Area with Convex Relaxation},
	booktitle = {NIPS},
	year = {2013},
	note = {Accepted},
	author = {Savchynskyy, Bogdan and J{\"o}rg H. Kappes and Swoboda, Paul and Christoph Schn{\"o}rr}
}
@conference {SavchynskyyNIPS2013,
	title = {Global MAP-Optimality by Shrinking the Combinatorial Search Area with Convex Relaxation},
	booktitle = {NIPS},
	year = {2013},
	note = {Accepted},
	author = {Savchynskyy, Bogdan and Kappes, Jorg Hendrik and Swoboda, Paul and Christoph Schn{\"o}rr}
}
@conference {SwobodaSSVM13,
	title = {Partial Optimality via Iterative Pruning for the Potts Model},
	booktitle = {Scale Space and Variational Methods (SSVM 2013)},
	year = {2013},
	author = {Swoboda, Paul and Savchynskyy, Bogdan and J{\"o}rg H. Kappes and Christoph Schn{\"o}rr}
}
@conference {LNCS80810321,
	title = {Variational Image Segmentation and Cosegmentation with the Wasserstein Distance},
	booktitle = {Energy Minimization Methods in Computer Vision and Pattern Recognition},
	volume = {8081},
	year = {2013},
	pages = {321--334},
	publisher = {Springer},
	organization = {Springer},
	isbn = {978-3-642-40394-1},
	author = {Swoboda, Paul and Christoph Schn{\"o}rr},
	editor = {Heyden, Anders and Kahl, Fredrik and Oskarsson, Magnus and Tai, Xue-Cheng and Olsson, Carl}
}
