scholarly journals Tree-width, clique-minors, and eigenvalues

2004 ◽  
Vol 274 (1-3) ◽  
pp. 281-287 ◽  
Author(s):  
Yuan Hong
Keyword(s):  
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.


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
Keyword(s):  

2004 ◽  
Vol 91 (1) ◽  
pp. 25-41 ◽  
Author(s):  
Matt DeVos ◽  
Guoli Ding ◽  
Bogdan Oporowski ◽  
Daniel P. Sanders ◽  
Bruce Reed ◽  
...  
Keyword(s):  

2020 ◽  
Vol 69 ◽  
pp. 231-295
Author(s):  
Peng Lin ◽  
Martin Neil ◽  
Norman Fenton

Performing efficient inference on high dimensional discrete Bayesian Networks (BNs) is challenging. When using exact inference methods the space complexity can grow exponentially with the tree-width, thus making computation intractable. This paper presents a general purpose approximate inference algorithm, based on a new region belief approximation method, called Triplet Region Construction (TRC). TRC reduces the cluster space complexity for factorized models from worst-case exponential to polynomial by performing graph factorization and producing clusters of limited size. Unlike previous generations of region-based algorithms, TRC is guaranteed to converge and effectively addresses the region choice problem that bedevils other region-based algorithms used for BN inference. Our experiments demonstrate that it also achieves significantly more accurate results than competing algorithms.


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