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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Dynamic Load Balancing Based on Constrained K-D Tree Decomposition for Parallel Particle Tracing

Particle tracing is a fundamental technique in flow field data visualization. In this work, we present a novel dynamic load balancing method for parallel particle tracing. Specifically, we employ a constrained k-d tree decomposition approach to dynamically redistribute tasks among processes. Each process is initially assigned a regularly partitioned block along with duplicated ghost layer under the memory limit. During particle tracing, the k-d tree decomposition is dynamically performed by constraining the cutting planes in the overlap range of duplicated data. This ensures that each process is reassigned particles as even as possible, and on the other hand the new assigned particles for a process always locate in its block. Result shows good load balance and high efficiency of our method.

Zhang, Jiang↗
DOE OSTI2018

Efficient tree decomposition of high-rank tensors [Efficient decomposition of high-rank tensors]

Tensors are a natural way to express correlations among many physical variables, but storing tensors in a computer naively requires memory which scales exponentially in the rank of the tensor. This is not optimal, as the required memory is actually set not by the rank but by the mutual information amongst the variables in question. Representations such as the tensor tree perform near-optimally when the tree decomposition is chosen to reflect the correlation structure in question, but making such a choice is non-trivial and good heuristics remain highly context-specific. In this work I present two new algorithms for choosing efficient tree decompositions, independent of the physical context of the tensor. The first is a brute-force algorithm which in most cases produces optimal decompositions but is generally impractical for high-rank tensors, as the number of possible choices grows exponentially in rank. Here, the second is a greedy algorithm, and while it is not optimal it performs extremely well in numerical experiments while having runtime which makes it practical even for tensors of very high rank.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Parallel Algorithms for Graph Optimization using Tree Decompositions

Although many NP-hard graph optimization problems can be solved in polynomial time on graphs of bounded tree-width, the adoption of these techniques into mainstream scientific computation has been limited due to the high memory requirements of required dynamic programming tables and excessive running times of sequential implementations. This work addresses both challenges by proposing a set of new parallel algorithms for all steps of a tree-decomposition based approach to solve maximum weighted independent set. A hybrid OpenMP/MPI implementation includes a highly scalable parallel dynamic programming algorithm leveraging the MADNESS task-based runtime, and computational results demonstrate scaling. This work enables a significant expansion of the scale of graphs on which exact solutions to maximum weighted independent set can be obtained, and forms a framework for solving additional graph optimization problems with similar techniques.

Weerapurage, Dinesh P↗
DOE OSTI2012

Parallel Algorithms for Graph Optimization Using Tree Decompositions

Although many $\cal{NP}$-hard graph optimization problems can be solved in polynomial time on graphs of bounded tree-width, the adoption of these techniques into mainstream scientific computation has been limited due to the high memory requirements of the necessary dynamic programming tables and excessive runtimes of sequential implementations. This work addresses both challenges by proposing a set of new parallel algorithms for all steps of a tree decomposition-based approach to solve the maximum weighted independent set problem. A hybrid OpenMP/MPI implementation includes a highly scalable parallel dynamic programming algorithm leveraging the MADNESS task-based runtime, and computational results demonstrate scaling. This work enables a significant expansion of the scale of graphs on which exact solutions to maximum weighted independent set can be obtained, and forms a framework for solving additional graph optimization problems with similar techniques.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2017

Efficient Delaunay Tessellation through K-D Tree Decomposition

Delaunay tessellations are fundamental data structures in computational geometry. They are important in data analysis, where they can represent the geometry of a point set or approximate its density. The algorithms for computing these tessellations at scale perform poorly when the input data is unbalanced. We investigate the use of k-d trees to evenly distribute points among processes and compare two strategies for picking split points between domain regions. Because resulting point distributions no longer satisfy the assumptions of existing parallel Delaunay algorithms, we develop a new parallel algorithm that adapts to its input and prove its correctness. We evaluate the new algorithm using two late-stage cosmology datasets. The new running times are up to 50 times faster using k-d tree compared with regular grid decomposition. Moreover, in the unbalanced data sets, decomposing the domain into a k-d tree is up to five times faster than decomposing it into a regular grid.

Morozov, Dmitriy↗
DOE OSTI2012

INDDGO: Integrated Network Decomposition & Dynamic programming for Graph Optimization

It is well-known that dynamic programming algorithms can utilize tree decompositions to provide a way to solve some NP -hard problems on graphs where the complexity is polynomial in the number of nodes and edges in the graph, but exponential in the width of the underlying tree decomposition. However, there has been relatively little computational work done to determine the practical utility of such dynamic programming algorithms. We have developed software to construct tree decompositions using various heuristics and have created a fast, memory-efficient dynamic programming implementation for solving maximum weighted independent set. We describe our software and the algorithms we have implemented, focusing on memory saving techniques for the dynamic programming. We compare the running time and memory usage of our implementation with other techniques for solving maximum weighted independent set, including a commercial integer programming solver and a semi-definite programming solver. Our results indicate that it is possible to solve some instances where the underlying decomposition has width much larger than suggested by the literature. For certain types of problems, our dynamic programming code runs several times faster than these other methods.

Groër, Christopher S.↗
DOE OSTI2021

Asynchronous and Load-Balanced Union-Find for Distributed and Parallel Scientific Data Visualization and Analysis

We present a novel distributed union-find algorithm that features asynchronous parallelism and k-d tree based load balancing for scalable visualization and analysis of scientific data. Applications of union-find include level set extraction and critical point tracking, but distributed union-find can suffer from high synchronization costs and imbalanced workloads across parallel processes. In this study, we prove that global synchronizations in existing distributed union-find can be eliminated without changing final results, allowing overlapped communications and computations for scalable processing. We also use a k-d tree decomposition to redistribute inputs, in order to improve workload balancing. We benchmark the scalability of our algorithm with up to 1,024 processes using both synthetic and application data. Here, we demonstrate the use of our algorithm in critical point tracking and super-level set extraction with high-speed imaging experiments and fusion plasma simulations, respectively.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Benchmarking treewidth as a practical component of tensor network simulations

Tensor networks are powerful factorization techniques which reduce resource requirements for numerically simulating principal quantum many-body systems and algorithms. The computational complexity of a tensor network simulation depends on the tensor ranks and the order in which they are contracted. Unfortunately, computing optimal contraction sequences (orderings) in general is known to be a computationally difficult (NP-complete) task. In 2005, Markov and Shi showed that optimal contraction sequences correspond to optimal (minimum width) tree decompositions of a tensor network’s line graph, relating the contraction sequence problem to a rich literature in structural graph theory. While treewidth-based methods have largely been ignored in favor of dataset-specific algorithms in the prior tensor networks literature, we demonstrate their practical relevance for problems arising from two distinct methods used in quantum simulation: multi-scale entanglement renormalization ansatz (MERA) datasets and quantum circuits generated by the quantum approximate optimization algorithm (QAOA). We exhibit multiple regimes where treewidth-based algorithms outperform domain-specific algorithms, while demonstrating that the optimal choice of algorithm has a complex dependence on the network density, expected contraction complexity, and user run time requirements. We further provide an open source software framework designed with an emphasis on accessibility and extendability, enabling replicable experimental evaluations and future exploration of competing methods by practitioners.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Distributed Augmentation, Hypersweeps, and Branch Decomposition of Contour Trees for Scientific Exploration

Contour trees describe the topology of level sets in scalar fields and are widely used in topological data analysis and visualization. A main challenge of utilizing contour trees for large-scale scientific data is their computation at scale using highperformance computing. To address this challenge, recent work has introduced distributed hierarchical contour trees for distributed computation and storage of contour trees. However, effective use of these distributed structures in analysis and visualization requires subsequent computation of geometric properties and branch decomposition to support contour extraction and exploration. In this work, we introduce distributed algorithms for augmentation, hypersweeps, and branch decomposition that enable parallel computation of geometric properties, and support the use of distributed contour trees as query structures for scientific exploration. Finally, we evaluate the parallel performance of these algorithms and apply them to identify and extract important contours for scientific visualization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Arbuscular mycorrhizal trees cause a higher carbon to nitrogen ratio of soil organic matter decomposition via rhizosphere priming than ectomycorrhizal trees

Tree roots and their associated microbes can significantly influence soil organic matter (SOM) decomposition, i.e., the rhizosphere priming effect. This effect is expected to be greater in trees associated with arbuscular mycorrhizal (AM) fungi, which produce higher extracellular enzymes especially surrounding hyphae, than in trees associated with ectomycorrhizal (ECM) fungi. In this work, we selected five tree species associated with AM (Juglans mandshurica Maxim. and Cunninghamia lanceolata (Lamb.) Hook.) or ECM (Picea koraiensis Nakai, Quercus mongolica Fischer ex Turcz. and Larix kaempferi (Lamb.) Carriere). We grew tree seedlings inside of cores lined with different mesh sizes to investigate how roots, hyphae and exudates influence soil carbon (C) and nitrogen (N) mineralization via the rhizosphere priming effect, using a 13 C natural abundance approach and a 15 N pool dilution method, concurrently. We found that tree seedlings significantly accelerated soil C decomposition by on average 78%, i.e., positive priming, compared to unplanted control pots. AM-associated trees induced 2.1 times greater soil C decomposition than ECM-associated trees across all mesh sizes. In contrast, gross N mineralization did not differ between tree-mycorrhizal associations. Compared to ECM counterparts, AM-associated trees had higher C- and lower N-degrading enzyme activities. Consequently, AM-associated trees induced a significantly higher C:N ratio of SOM decomposition than their ECM counterparts, which could be associated with the differences in soil enzyme activities for C and N degradation. Further, for both AM- and ECM-associated trees, we found no significant influences of mesh size on soil C decomposition, suggesting that the rhizosphere priming effect of mycorrhizal symbiosis was predominantly driven by root exudates. We conclude that SOM decomposition caused by AM-associated trees may have a higher C:N ratio than that by ECM-associated trees mainly due to differences in microbial enzyme investment. Our findings imply that tree-mycorrhizal associations are capable of modulating soil biogeochemical cycling via the rhizosphere priming effect.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2013

Combinatorial geometry domain decomposition strategies for Monte Carlo simulations

Analysis and modeling of nuclear reactors can lead to memory overload for a single core processor when it comes to refined modeling. A method to solve this problem is called 'domain decomposition'. In the current work, domain decomposition algorithms for a combinatorial geometry Monte Carlo transport code are developed on the JCOGIN (J Combinatorial Geometry Monte Carlo transport INfrastructure). Tree-based decomposition and asynchronous communication of particle information between domains are described in the paper. Combination of domain decomposition and domain replication (particle parallelism) is demonstrated and compared with that of MERCURY code. A full-core reactor model is simulated to verify the domain decomposition algorithms using the Monte Carlo particle transport code JMCT (J Monte Carlo Transport Code), which has being developed on the JCOGIN infrastructure. Besides, influences of the domain decomposition algorithms to tally variances are discussed. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Performance of modern color decompositions for standard candle LHC tree amplitudes

In the last decade, developments of matrix element and phase space generators have focused on providing good efficiency and maximal flexibility and automation for a wide range of physical processes. However, as recent studies have shown, they are a major bottleneck in the established Monte Carlo event generator toolchains. With the advent of the HL-LHC and ever rising precision requirements, future developments will need to focus on computational performance, especially at intermediate to large jet multiplicities. We present the novel BlockGen family of fast matrix element algorithms that are amenable for GPU acceleration, making use of modern, minimal color decompositions. Moreover, we discuss the performance achieved for standard candle processes such as V +jets and tt̄+jets production.

Bothmann, E. [Gottingen U.]↗
DOE OSTI2017

The Approximability of Partial Vertex Covers in Trees.

Motivated by applications in risk management of computational systems, we focus our attention on a special case of the partial vertex cover problem, where the underlying graph is assumed to be a tree. Here, we consider four possible versions of this setting, depending on whether vertices and edges are weighted or not. Two of these versions, where edges are assumed to be unweighted, are known to be polynomial-time solvable (Gandhi, Khuller, and Srinivasan, 2004). However, the computational complexity of this problem with weighted edges, and possibly with weighted vertices, has not been determined yet. The main contribution of this paper is to resolve these questions, by fully characterizing which variants of partial vertex cover remain intractable in trees, and which can be efficiently solved. In particular, we propose a pseudo-polynomial DP-based algorithm for the most general case of having weights on both edges and vertices, which is proven to be NPhard. This algorithm provides a polynomial-time solution method when weights are limited to edges, and combined with additional scaling ideas, leads to an FPTAS for the general case. A secondary contribution of this work is to propose a novel way of using centroid decompositions in trees, which could be useful in other settings as well.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Climatic controls of decomposition drive the global biogeography of forest-tree symbioses

The identity of the dominant microbial symbionts in a forest determines the ability of trees to access limiting nutrients from atmospheric or soil pools, sequester carbon and withstand the impacts of climate change. Characterizing the global distribution of symbioses, and identifying the factors that control it, are thus integral to understanding present and future forest ecosystem functioning. In this work we generate the first spatially explicit global map of forest symbiotic status using a database of over 1.1 million forest inventory plots with over 28,000 tree species. Our analyses indicate that climatic variables, and in particular climatically-controlled variation in decomposition rate, are the primary drivers of the global distribution of major symbioses. We estimate that ectomycorrhizal (EM) trees, which represent only 2% of all plant species, constitute approximately 60% of tree stems on Earth. EM symbiosis dominates forests where seasonally cold and dry climates inhibit decomposition, and are the predominant symbiosis at high latitudes and elevation. On the other hand, arbuscular mycorrhizal (AM) trees dominate aseasonally warm tropical forests and occur with EM trees in temperate biomes where seasonally warm-and-wet climates enhance decomposition. Continental transitions between AM and EM dominated forests occur relatively abruptly along climate driven decomposition gradients, which is likely caused by positive plant-microbe feedbacks. Symbiotic N-fixers, which are insensitive to climatic controls on decomposition compared with mycorrhizal fungi, are most abundant in arid biomes with alkaline soils and high maximum temperatures. The climatically driven global symbiosis gradient we document represents the first spatially-explicit, quantitative understanding of microbial symbioses at the global scale and demonstrates the critical role of microbial mutualisms in shaping the distribution of plant species.

59 BASIC BIOLOGICAL SCIENCES↗