Homogeneity vs. Adjacency: Generalising Some Graph Decomposition Algorithms

International audience A factorizing permutation of a given graph is simply a permutation of the vertices in which all decomposition sets appear to be factors. Such a concept seems to play a central role in recent papers dealing with graph decomposition. It is applied here for modular decomposition and we propose a linear algorithm that computes the whole decomposition tree when a factorizing permutation is provided. This algorithm can be seen as a common generalization of Ma and Hsu for modular decomposition of chordal graphs and Habib, Huchard and Spinrad for inheritance graphs decomposition. It also suggests many new decomposition algorithms for various notions of graph decompositions.

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Implementation of Domain Decomposition and Data Decomposition Algorithms in RMC code

SNA + MC 2013 - Joint International Conference on Supercomputing in Nuclear Applications + Monte Carlo ◽

10.1051/snamc/201404201 ◽

2014 ◽

Author(s):

Jin’gang Liang ◽

Yun Cai ◽

Kan Wang ◽

Ding She

Keyword(s):

Domain Decomposition ◽

Decomposition Algorithms ◽

Data Decomposition

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Decomposition of tasks in a group of robots using cloud computing technologies

Proceedings of the Mavlyutov Institute of Mechanics ◽

10.21662/uim2017.1.012 ◽

2017 ◽

Vol 12 (1) ◽

pp. 83-88

Author(s):

O.V. Darintsev ◽

A.B. Migranov

Keyword(s):

Cloud Computing ◽

Experimental Verification ◽

Decomposition Algorithms ◽

Complex Task ◽

Large Problem ◽

Working Capacity ◽

Linear Distribution ◽

Effective Teams ◽

Computing Technologies

In this paper, various variants of decomposition of tasks in a group of robots using cloud computing technologies are considered. The specifics of the field of application (teams of robots) and solved problems are taken into account. In the process of decomposition, the solution of one large problem is divided into a solution of a series of smaller, simpler problems. Three ways of decomposition based on linear distribution, swarm interaction and synthesis of solutions are proposed. The results of experimental verification of the developed decomposition algorithms are presented, the working capacity of methods for planning trajectories in the cloud is shown. The resulting solution is a component of the complex task of building effective teams of robots.

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ShadingNet: Image Intrinsics by Fine-Grained Shading Decomposition

International Journal of Computer Vision ◽

10.1007/s11263-021-01477-5 ◽

2021 ◽

Author(s):

Anil S. Baslamisli ◽

Partha Das ◽

Hoang-An Le ◽

Sezer Karaoglu ◽

Theo Gevers

Keyword(s):

Neural Network ◽

Large Scale ◽

State Of The Art ◽

Image Decomposition ◽

Natural Environments ◽

Decomposition Algorithms ◽

Ambient Light ◽

Fine Grained ◽

Large Scale Dataset ◽

Direct Illumination

AbstractIn general, intrinsic image decomposition algorithms interpret shading as one unified component including all photometric effects. As shading transitions are generally smoother than reflectance (albedo) changes, these methods may fail in distinguishing strong photometric effects from reflectance variations. Therefore, in this paper, we propose to decompose the shading component into direct (illumination) and indirect shading (ambient light and shadows) subcomponents. The aim is to distinguish strong photometric effects from reflectance variations. An end-to-end deep convolutional neural network (ShadingNet) is proposed that operates in a fine-to-coarse manner with a specialized fusion and refinement unit exploiting the fine-grained shading model. It is designed to learn specific reflectance cues separated from specific photometric effects to analyze the disentanglement capability. A large-scale dataset of scene-level synthetic images of outdoor natural environments is provided with fine-grained intrinsic image ground-truths. Large scale experiments show that our approach using fine-grained shading decompositions outperforms state-of-the-art algorithms utilizing unified shading on NED, MPI Sintel, GTA V, IIW, MIT Intrinsic Images, 3DRMS and SRD datasets.

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Parallel Iterative Linear Equation Solvers: An Investigation of Domain Decomposition Algorithms for Reservoir Simulation

10.2118/16021-ms ◽

1987 ◽

Cited By ~ 8

Author(s):

J.E. Killough ◽

M.F. Wheeler

Keyword(s):

Domain Decomposition ◽

Linear Equation ◽

Reservoir Simulation ◽

Decomposition Algorithms ◽

Parallel Iterative

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Robust Template Decomposition without Weight Restriction for Cellular Neural Networks Implementing Arbitrary Boolean Functions Using Support Vector Classifiers

Mathematical Problems in Engineering ◽

10.1155/2013/614543 ◽

2013 ◽

Vol 2013 ◽

pp. 1-9

Author(s):

Yih-Lon Lin ◽

Jer-Guang Hsieh ◽

Jyh-Horng Jeng

Keyword(s):

Neural Networks ◽

Boolean Function ◽

Past Research ◽

Cellular Neural Network ◽

Decomposition Methods ◽

Cellular Neural Networks ◽

Support Vector ◽

Decomposition Algorithms ◽

Weight Restriction ◽

The Given

If the given Boolean function is linearly separable, a robust uncoupled cellular neural network can be designed as a maximal margin classifier. On the other hand, if the given Boolean function is linearly separable but has a small geometric margin or it is not linearly separable, a popular approach is to find a sequence of robust uncoupled cellular neural networks implementing the given Boolean function. In the past research works using this approach, the control template parameters and thresholds are restricted to assume only a given finite set of integers, and this is certainly unnecessary for the template design. In this study, we try to remove this restriction. Minterm- and maxterm-based decomposition algorithms utilizing the soft margin and maximal margin support vector classifiers are proposed to design a sequence of robust templates implementing an arbitrary Boolean function. Several illustrative examples are simulated to demonstrate the efficiency of the proposed method by comparing our results with those produced by other decomposition methods with restricted weights.

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