Vertex partitioning problems on graphs with bounded tree width

Author(s):  
N.R. Aravind ◽  
Subrahmanyam Kalyanasundaram ◽  
Anjeneya Swami Kare
2021 ◽  
Vol 5 (1) ◽  
pp. 14
Author(s):  
Christos Makris ◽  
Georgios Pispirigos

Nowadays, due to the extensive use of information networks in a broad range of fields, e.g., bio-informatics, sociology, digital marketing, computer science, etc., graph theory applications have attracted significant scientific interest. Due to its apparent abstraction, community detection has become one of the most thoroughly studied graph partitioning problems. However, the existing algorithms principally propose iterative solutions of high polynomial order that repetitively require exhaustive analysis. These methods can undoubtedly be considered resource-wise overdemanding, unscalable, and inapplicable in big data graphs, such as today’s social networks. In this article, a novel, near-linear, and highly scalable community prediction methodology is introduced. Specifically, using a distributed, stacking-based model, which is built on plain network topology characteristics of bootstrap sampled subgraphs, the underlined community hierarchy of any given social network is efficiently extracted in spite of its size and density. The effectiveness of the proposed methodology has diligently been examined on numerous real-life social networks and proven superior to various similar approaches in terms of performance, stability, and accuracy.


Agronomy ◽  
2019 ◽  
Vol 9 (11) ◽  
pp. 741 ◽  
Author(s):  
Haihui Yang ◽  
Xiaochan Wang ◽  
Guoxiang Sun

Perception of the fruit tree canopy is a vital technology for the intelligent control of a modern standardized orchard. Due to the complex three-dimensional (3D) structure of the fruit tree canopy, morphological parameters extracted from two-dimensional (2D) or single-perspective 3D images are not comprehensive enough. Three-dimensional information from different perspectives must be combined in order to perceive the canopy information efficiently and accurately in complex orchard field environment. The algorithms used for the registration and fusion of data from different perspectives and the subsequent extraction of fruit tree canopy related parameters are the keys to the problem. This study proposed a 3D morphological measurement method for a fruit tree canopy based on Kinect sensor self-calibration, including 3D point cloud generation, point cloud registration and canopy information extraction of apple tree canopy. Using 32 apple trees (Yanfu 3 variety) morphological parameters of the height (H), maximum canopy width (W) and canopy thickness (D) were calculated. The accuracy and applicability of this method for extraction of morphological parameters were statistically analyzed. The results showed that, on both sides of the fruit trees, the average relative error (ARE) values of the morphological parameters including the fruit tree height (H), maximum tree width (W) and canopy thickness (D) between the calculated values and measured values were 3.8%, 12.7% and 5.0%, respectively, under the V1 mode; the ARE values under the V2 mode were 3.3%, 9.5% and 4.9%, respectively; and the ARE values under the V1 and V2 merged mode were 2.5%, 3.6% and 3.2%, respectively. The measurement accuracy of the tree width (W) under the double visual angle mode had a significant advantage over that under the single visual angle mode. The 3D point cloud reconstruction method based on Kinect self-calibration proposed in this study has high precision and stable performance, and the auxiliary calibration objects are readily portable and easy to install. It can be applied to different experimental scenes to extract 3D information of fruit tree canopies and has important implications to achieve the intelligent control of standardized orchards.


1999 ◽  
Vol 90 (1-3) ◽  
pp. 27-50 ◽  
Author(s):  
Jonathan W Berry ◽  
Mark K Goldberg

1979 ◽  
Vol 101 (1) ◽  
pp. 17-22 ◽  
Author(s):  
K. Phillips

A mathematical model for job scheduling in a specified context is presented. The model uses both linear programming and combinatorial methods. While designed with a view toward optimization of scheduling of facility and plant operations at the Deep Space Network (DSN) Station at Goldstone, the context is sufficiently general to be widely applicable. The general scheduling problem including options for scheduling objectives is discussed and fundamental parameters identified. Mathematical algorithms for partitioning problems germaine to scheduling are presented. A more detailed description of algorithms and of operational aspects of the model is planned for a later report.


2002 ◽  
Vol 11 (6) ◽  
pp. 541-547 ◽  
Author(s):  
PATRICK BELLENBAUM ◽  
REINHARD DIESTEL

We give short proofs of the following two results: Thomas's theorem that every finite graph has a linked tree-decomposition of width no greater than its tree-width; and the ‘tree-width duality theorem’ of Seymour and Thomas, that the tree-width of a finite graph is exactly one less than the largest order of its brambles.


2007 ◽  
Vol 51 (3) ◽  
pp. 326-362 ◽  
Author(s):  
P. Hlineny ◽  
S.-i. Oum ◽  
D. Seese ◽  
G. Gottlob
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