Mujika Aramendia, Asier · Communities in ADDI (University of the Basque Country) · 2015
In this work I present recent scientific papers related to the concept of tree-depth: different \ncharacterizations, a game theoretic approach to it and recently discovered applications. \nThe focus in this work is presenting all the ideas in a self-contained way, such that they \ncan be easily understood with little previous knowledge. Apart from that all the ideas are \npresented in a homogeneous way with clear examples and all the lemmas, some of which \ndidn’t have proofs in the papers, are presented with rigorous proofs.
Cited by 0Open access
Matt DeVos, O‐joung Kwon, Sang‐il Oum · European Journal of Combinatorics · 2020
Cited by 16Open access
Jaeho Lee, Kangjin Kim, Gyeong Taek Lee · ArXiv.org · 2025
This paper proposes the Next-Depth Lookahead Tree (NDLT), a single-tree model designed to improve performance by evaluating node splits not only at the node being optimized but also by evaluating the quality of the next depth level.
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Sara Silva, Jonas S. Almeida · Lecture notes in computer science · 2003
Cited by 44
Zdenĕk Dvořák, Archontia C. Giannopoulou, Dimitrios M. Thilikos · European Journal of Combinatorics · 2011
Cited by 39
Yves Baumann, Tal Ben‐Nun, Maciej Besta et al. · arXiv (Cornell University) · 2024
Contemporary accelerator designs exhibit a high degree of spatial localization, wherein two-dimensional physical distance determines communication costs between processing elements. This situation presents considerable algorithmic challenges, particularly when managing sparse data, a pivotal component in progressing data science. The spatial computer model quantifies communication locality by weighting processor communication costs by distance, introducing a term named energy. Moreover, it integrates depth, a widely-utilized metric, to promote high parallelism. We propose and analyze a framework for efficient spatial tree algorithms within the spatial computer model. Our primary method constructs a spatial tree layout that optimizes the locality of the neighbors in the compute grid. This approach thereby enables locality-optimized messaging within the tree. Our layout achieves a polynomial factor improvement in energy compared to utilizing a PRAM approach. Using this layout, we develop energy-efficient treefix sum and lowest common ancestor algorithms, which are both fundamental building blocks for other graph algorithms. With high probability, our algorithms exhibit near-linear energy and poly-logarithmic depth. Our contributions augment a growing body of work demonstrating that computations can have both high spatial locality and low depth. Moreover, our work constitutes an advancement in the spatial layout of irregular and sparse computations.
Cited by 0Open access
Felix Gaisbauer (10451821), Armin Pournaki (7536350), Sven Banisch (10451824) et al. · Figshare · 2021
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Petr Hliněný, O‐joung Kwon, Jan Óbdržálek et al. · arXiv (Cornell University) · 2014
In a recent paper, Kwon and Oum claim that every graph of bounded rank-width is a pivot-minor of a graph of bounded tree-width (while the converse has been known true already before). We study the analogous questions for "depth" parameters of graphs, namely for the tree-depth and related new shrub-depth. We show that shrub-depth is monotone under taking vertex-minors, and that every graph class of bounded shrub-depth can be obtained via vertex-minors of graphs of bounded tree-depth. We also consider the same questions for bipartite graphs and pivot-minors.
Cited by 0Open access
Yves Baumann, Tal Ben‐Nun, Maciej Besta et al. · 2024
Contemporary accelerator designs exhibit a high degree of spatial localization, wherein two-dimensional physical distance determines communication costs between processing elements. This situation presents considerable algorithmic challenges, particularly when managing sparse data, a pivotal component in progressing data science. The spatial computer model quantifies communication locality by weighting processor communication costs by distance, introducing a term named energy. Moreover, it integrates depth, a widely-utilized metric, to promote high parallelism. We propose and analyze a framework for efficient spatial tree algorithms within the spatial computer model. Our primary method constructs a spatial tree layout that optimizes the locality of the neighbors in the compute grid. This approach thereby enables locality-optimized messaging within the tree. Our layout achieves a polynomial factor improvement in energy compared to utilizing a PRAM approach. Using this layout, we develop energy-efficient treefix sum and lowest common ancestor algorithms, which are both fundamental building blocks for other graph algorithms. With high probability, our algorithms exhibit near-linear energy and poly-logarithmic depth. Our contributions augment a growing body of work demonstrating that computations can have both high spatial locality and low depth. Moreover, our work constitutes an advancement in the spatial layout of irregular and sparse computations.
Cited by 2
Petr Hliněný, O‐joung Kwon, Jan Óbdržálek et al. · European Journal of Combinatorics · 2016
Cited by 7
Nelson H. F. Beebe · 2014
Cited by 0
Ojas Parekh, R. Ravi, Michael Zlatin · Operations Research Letters · 2022
Cited by 2Open access
Ardvin Kester S. Ong (14636918), Yogi Tri Prasetyo (14636921), Atheena Rhezelle B. Manguray (15674952) et al. · Figshare · 2023
<div><p>Samgyeopsal has become a widely popular cuisine in the Philippines since 2014. The rise of Samgyeopsal is evident worldwide as it is available in countries such as the United States, Northern, and Southern Asia. This study aimed to explore the intention to eat Samgyeopsal during the COVID-19 pandemic utilizing structural equation modeling and random forest classifier. With a total of 1014 responses collected online, the result showed that utilitarian and hedonic motivation, Korean influence, and attitude led to very high actual behavior in east Samgyeopsal in the Philippines. Moreover, subjective norm, perceived behavioral control, and intention led to significant results influencing intention to actual behavior. Lastly, the COVID-19 safety protocol showed the least significant result. This study is the first study that evaluated the intention of consumers to eat Samgyeopsal in the Philippines during the COVID-19 pandemic. The results of this study would be beneficial to Korean BBQ restaurateurs and the further development of their marketing strategies even in other countries. Finally, the model construct of this study can be extended and applied in evaluating the consumers’ eating intention toward other varieties of food or cuisines worldwide.</p></div>
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Darrel L. Sparks · Journal of American Pomological Society · 2005
Hurricanes Frances, Ivan, and Jeanne inflicted widespread damage to pecan [ Carya illinoinensis(Wangenh.) K. Koch] trees in Georgia during September 2004. Tree damage was either limb breakage, uprooting, or varying degrees of tree tilting without uprooting. The relationship of degree of tree tilt to setting depth at planting was examined. Trees that were set at the same level at which they grew in the nursery did not tilt. Tilting of trees which had been set at a lower depth ranged from a few degrees from upright to total blow over.
Cited by 0Open access
Gavin Lee Goodship · Zenodo (CERN European Organization for Nuclear Research) · 2026
Rooted-Tree Backpropagation at Extreme Depth This repository demonstrates stable training of extremely deep residual networks (up to 4,000 residual blocks, approximately 517 million parameters) on commodity laptop hardware using a single 5.77 GB GPU. The approach combines aggressive activation checkpointing with a rooted-tree–aware modification of backpropagation, enabling learning in regimes where standard training typically becomes unstable. At extreme depth, backpropagation behaves as a truncated numerical expansion of the true gradient flow; selectively restoring second-order rooted-tree terms via Hessian–vector products, while pruning them to the terminal layers where stiffness concentrates, yields stable and well-conditioned optimization. Empirically, a 4,000-layer CIFAR-10 ResNet reaches 57.5% test accuracy after epoch 0, 66.8% after epoch 1, and 75.9% after epoch 2, with zero curvature-skip events, using a true batch size of 8 and no gradient accumulation. This release is intended as a research artifact supporting reproducibility and further study of numerical stability, optimization dynamics, and solver-aware learning at extreme depth.
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Mark W. Jarecki, J. Szykman, Gary J. Kling · HortScience · 2006
Growers, nurseries, landscape contractors and installers, and those responsible for maintenance have observed a trend that trees are too deep within the root ball. This study addresses the relationship between planting depth and its effect on tree survival, root growth, root architecture, and caliper growth. The experiment was initiated to determine the effect of planting depth on nursery-grown trees. Three-year-old, 2.1–2.7 m, bare-root liners of Acer platanoides `Emerald Lustre', Fraxinus americana `Autumn Purple', Fraxinus pennsylvanica `Patmore', and Gleditsia triacanthos f. inermis `Shade Master' were planted in April 2004 in a completely randomized design with 20 replications per treatment per species. The trees were selected so that the distance between the graft union and the trunk flare was consistent. Trees were planted with the graft union 15.2 cm below the soil surface, or with the base of the graft union at the finished grade or with the trunk flare at the finished grade. The trees were grown in a nursery field setting with minimal supplemental watering. There were no differences in stem caliper growth at the end of two seasons in any of the four species. Root dry mass, stem elongation, and rooting structure were determined on a representative sample of trees while others were planted into the landscape for a long-term study of the effects of the original planting depth on landscape performance.
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Jaroslav Nešetřil, Patrice Ossona de Mendez · Algorithms and combinatorics · 2012
Cited by 18
Gavin Lee Goodship · Zenodo (CERN European Organization for Nuclear Research) · 2026
Rooted-Tree Backpropagation at Extreme Depth This repository demonstrates stable training of extremely deep residual networks (up to 4,000 residual blocks, approximately 517 million parameters) on commodity laptop hardware using a single 5.77 GB GPU. The approach combines aggressive activation checkpointing with a rooted-tree–aware modification of backpropagation, enabling learning in regimes where standard training typically becomes unstable. At extreme depth, backpropagation behaves as a truncated numerical expansion of the true gradient flow; selectively restoring second-order rooted-tree terms via Hessian–vector products, while pruning them to the terminal layers where stiffness concentrates, yields stable and well-conditioned optimization. Empirically, a 4,000-layer CIFAR-10 ResNet reaches 57.5% test accuracy after epoch 0, 66.8% after epoch 1, and 75.9% after epoch 2, with zero curvature-skip events, using a true batch size of 8 and no gradient accumulation. This release is intended as a research artifact supporting reproducibility and further study of numerical stability, optimization dynamics, and solver-aware learning at extreme depth.
Cited by 0Open access
Piotr Borowiecki, Dariusz Dereniowski, Dorota Osula · Theoretical Computer Science · 2023
Cited by 0
David Cortés‐Polo · arXiv (Cornell University) · 2021
The isolation forest algorithm for outlier detection exploits a simple yet effective observation: if taking some multivariate data and making uniformly random cuts across the feature space recursively, it will take fewer such random cuts for an outlier to be left alone in a given subspace as compared to regular observations. The original idea proposed an outlier score based on the tree depth (number of random cuts) required for isolation, but experiments here show that using information about the size of the feature space taken and the number of points assigned to it can result in improved results in many situations without any modification to the tree structure, especially in the presence of categorical features.
Cited by 2Open access