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We consider move-making algorithms for energy minimization of multi-label Markov Random Fields (MRFs). Since this is not a tractable problem in general, a commonly used heuristic is to minimize over subsets of labels and variables in an…

Computer Vision and Pattern Recognition · Computer Science 2018-11-26 Richard Hartley , Thalaiyasingam Ajanthan

In this paper, we address the minimum-cost node-capacitated multiflow problem in an undirected network. For this problem, Babenko and Karzanov (2012) showed strongly polynomial-time solvability via the ellipsoid method. Our result is the…

Data Structures and Algorithms · Computer Science 2019-09-05 Hiroshi Hirai , Motoki Ikeda

In this paper, we develop an $O((m \log k) {\rm MSF} (n,m,1))$-time algorithm to find a half-integral node-capacitated multiflow of the maximum total flow-value in a network with $n$ nodes, $m$ edges, and $k$ terminals, where ${\rm MSF}…

Data Structures and Algorithms · Computer Science 2018-10-30 Hiroshi Hirai

Towards the development of 6G mobile networks, it is promising to integrate a large number of devices from multi-dimensional platforms, and it is crucial to have a solid understanding of the theoretical limits of large-scale networks. We…

Information Theory · Computer Science 2025-09-19 Yanxiao Liu , Shenghao Yang , Cheuk Ting Li

Scalable high-quality MAP inference in arbitrary-order Markov Random Fields (MRFs) remains challenging. Approximate message-passing methods are often efficient but can degrade on dense or high-order instances, while exact solvers such as…

Machine Learning · Computer Science 2026-05-08 Yaomin Wang , Chaolong Ying , Xiaodong Luo , Tianshu Yu

In this paper a high speed neural network classifier based on extreme learning machines for multi-label classification problem is proposed and dis-cussed. Multi-label classification is a superset of traditional binary and multi-class…

Machine Learning · Computer Science 2016-09-06 Meng Joo Er , Rajasekar Venkatesan , Ning Wang

We consider the problem of jointly inferring the M-best diverse labelings for a binary (high-order) submodular energy of a graphical model. Recently, it was shown that this problem can be solved to a global optimum, for many practically…

Computer Vision and Pattern Recognition · Computer Science 2016-06-24 Alexander Kirillov , Alexander Shekhovtsov , Carsten Rother , Bogdan Savchynskyy

Multi-region segmentation algorithms often have the onus of incorporating complex anatomical knowledge representing spatial or geometric relationships between objects, and general-purpose methods of addressing this knowledge in an…

Computer Vision and Pattern Recognition · Computer Science 2014-06-09 John S. H. Baxter , Martin Rajchl , Jing Yuan , Terry M. Peters

The problem of minimizing the Potts energy function frequently occurs in computer vision applications. One way to tackle this NP-hard problem was proposed by Kovtun [19,20]. It identifies a part of an optimal solution by running $k$ maxflow…

Computer Vision and Pattern Recognition · Computer Science 2013-10-08 Igor Gridchyn , Vladimir Kolmogorov

There are many problems in machine learning and data mining which are equivalent to selecting a non-redundant, high "quality" set of objects. Recommender systems, feature selection, and data summarization are among many applications of…

Machine Learning · Computer Science 2019-04-19 Mehrdad Ghadiri , Mark Schmidt

We study two mixed robust/average-case submodular partitioning problems that we collectively call Submodular Partitioning. These problems generalize both purely robust instances of the problem (namely max-min submodular fair allocation…

Data Structures and Algorithms · Computer Science 2016-08-17 Kai Wei , Rishabh Iyer , Shengjie Wang , Wenruo Bai , Jeff Bilmes

We study a general class of convex submodular optimization problems with indicator variables. Many applications such as the problem of inferring Markov random fields (MRFs) with a sparsity or robustness prior can be naturally modeled in…

Optimization and Control · Mathematics 2025-07-09 Shaoning Han , Andrés Gómez

We propose a new algorithm to obtain max flow for the multicommodity flow. This algorithm utilizes the max-flow min-cut theorem and the well known labeling algorithm due to Ford and Fulkerson [1]. We proceed as follows: We select one…

General Mathematics · Mathematics 2010-01-13 Dhananjay P. Mehendale

Resampling algorithms are a useful approach to deal with imbalanced learning in multilabel scenarios. These methods have to deal with singularities in the multilabel data, such as the occurrence of frequent and infrequent labels in the same…

Machine Learning · Computer Science 2025-01-22 Antonio J. Rivera , Miguel A. Dávila , David Elizondo , María J. del Jesus , Francisco Charte

The Maximum Flow (Max-Flow) problem is a cornerstone in graph theory and combinatorial optimization, aiming to determine the largest possible flow from a designated source node to a sink node within a capacitated flow network. It has…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-11-04 Shruthi Kannappan , Ashwina Kumar , Rupesh Nasre

We study a general class of convex submodular optimization problems with indicator variables. Many applications such as the problem of inferring Markov random fields (MRFs) with a sparsity or robustness prior can be naturally modeled in…

Optimization and Control · Mathematics 2025-07-08 Andres Gomez , Shaoning Han

While Markov Random Fields (MRFs) are widely used in computer vision, they present a quite challenging inference problem. MRF inference can be accelerated by pre-processing techniques like Dead End Elimination (DEE) or QPBO-based approaches…

Computer Vision and Pattern Recognition · Computer Science 2017-08-10 Chen Wang , Charles Herrmann , Ramin Zabih

The multi-label classification problem has generated significant interest in recent years. However, existing approaches do not adequately address two key challenges: (a) the ability to tackle problems with a large number (say millions) of…

Machine Learning · Computer Science 2013-11-26 Hsiang-Fu Yu , Prateek Jain , Purushottam Kar , Inderjit S. Dhillon

One issue limiting the adaption of large-scale multi-region segmentation is the sometimes prohibitive memory requirements. This is especially troubling considering advances in massively parallel computing and commercial graphics processing…

Computer Vision and Pattern Recognition · Computer Science 2015-02-02 John S. H. Baxter , Martin Rajchl , Jing Yuan , Terry M. Peters

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…

Computer Vision and Pattern Recognition · Computer Science 2017-02-06 Alexander Shekhovtsov , Paul Swoboda , Bogdan Savchynskyy
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