Tree Traversal Research Articles

A Cooperative Hunting Method for Multi-USV Based on the A* Algorithm in an Environment with Obstacles.

A single unmanned surface combatant (USV) has poor mission execution capability, so the cooperation of multiple unmanned surface ships is widely used. Cooperative hunting is an important aspect of multi USV collaborative research. Therefore, this paper proposed a cooperative hunting method for multi-USV based on the A* algorithm in an environment with obstacles. First, based on the traditional A* algorithm, a path smoothing method based on USV minimum turning radius is proposed. At the same time, the post order traversal recursive algorithm in the binary tree method is used to replace the enumeration algorithm to obtain the optimal path, which improves the efficiency of the A* algorithm. Second, a biomimetic multi USV swarm collaborative hunting method is proposed. Multiple USV clusters simulate the hunting strategy of lions to pre-form on the target's path, so multiple USV clusters do not require manual formation. During the hunting process, the formation of multiple USV groups is adjusted to limit the movement and turning of the target, thereby reducing the range of activity of the target and improving the effectiveness of the algorithm. To verify the effectiveness of the algorithm, two sets of simulation experiments were conducted. The results show that the algorithm has good performance in path planning and target search.

Lithological Classification by Hyperspectral Images Based on a Two-Layer XGBoost Model, Combined with a Greedy Algorithm

Lithology classification is important in mineral resource exploration, engineering geological exploration, and disaster monitoring. Traditional laboratory methods for the qualitative analysis of rocks are limited by sampling conditions and analytical techniques, resulting in high costs, low efficiency, and the inability to quickly obtain large-scale geological information. Hyperspectral remote sensing technology can classify and identify lithology using the spectral characteristics of rock, and is characterized by fast detection, large coverage area, and environmental friendliness, which provide the application potential for lithological mapping at a large regional scale. In this study, ZY1-02D hyperspectral images were used as data sources to construct a new two-layer extreme gradient boosting (XGBoost) lithology classification model based on the XGBoost decision tree and an improved greedy search algorithm. A total of 153 spectral bands of the preprocessed hyperspectral images were input into the first layer of the XGBoost model. Based on the tree traversal structural characteristics of the leaf nodes in the XGBoost model, three built-in XGBoost importance indexes were split and combined. The improved greedy search algorithm was used to extract the spectral band variables, which were imported into the second layer of the XGBoost model, and the bat algorithm was used to optimize the modeling parameters of XGBoost. The extraction model of rock classification information was constructed, and the classification map of regional surface rock types was drawn. Field verification was performed for the two-layer XGBoost rock classification model, and its accuracy and reliability were evaluated based on four indexes, namely, accuracy, precision, recall, and F1 score. The results showed that the two-layer XGBoost model had a good lithological classification effect, robustness, and adaptability to small sample datasets. Compared with the traditional machine learning model, the two-layer XGBoost model shows superior performance. The accuracy, precision, recall, and F1 score of the verification set were 0.8343, 0.8406, 0.8350, and 0.8157, respectively. The variable extraction ability of the constructed two-layer XGBoost model was significantly improved. Compared with traditional feature selection methods, the GREED-GFC method, when applied to the two-layer XGBoost model, contributes to more stable rock classification performance and higher lithology prediction accuracy, and the smallest number of extracted features. The lithological distribution information identified by the model was in good agreement with the lithology information verified in the field.

Fishburn trees

The in-order traversal provides a natural correspondence between binary trees with a decreasing vertex labeling and endofunctions on a finite set. By suitably restricting the vertex labeling we arrive at a class of trees that we call Fishburn trees. We give bijections between Fishburn trees and other well-known combinatorial structures that are counted by the Fishburn numbers, and by composing these new maps we obtain simplified versions of some of the known maps. Finally, we apply this new machinery to the so called flip and sum problems on modified ascent sequences.

GPU-parallelisation of Haar wavelet-based grid resolution adaptation for fast finite volume modelling: application to shallow water flows

Abstract Wavelet-based grid resolution adaptation driven by the ‘multiresolution analysis’ (MRA) of the Haar wavelet (HW) allows to devise an adaptive first-order finite volume (FV1) model (HWFV1) that can readily preserve the modelling fidelity of its reference uniform-grid FV1 counterpart. However, the MRA entails an enormous computational effort as it involves ‘encoding’ (coarsening), ‘decoding’ (refining), analysing and traversing modelled data across a deep hierarchy of nested, uniform grids. GPU-parallelisation of the MRA is needed to handle its computational effort, but its algorithmic structure (1) hinders coalesced memory access on the GPU and (2) involves an inherently sequential tree traversal problem. This work redesigns the algorithmic structure of the MRA in order to parallelise it on the GPU, addressing (1) by applying Z-order space-filling curves and (2) by adopting a parallel tree traversal algorithm. This results in a GPU-parallelised HWFV1 model (GPU-HWFV1). GPU-HWFV1 is verified against its CPU predecessor (CPU-HWFV1) and its GPU-parallelised reference uniform-grid counterpart (GPU-FV1) over five shallow water flow test cases. GPU-HWFV1 preserves the modelling fidelity of GPU-FV1 while being up to 30 times faster. Compared to CPU-HWFV1, it is up to 200 times faster, suggesting that the GPU-parallelised MRA could be used to speed up other FV1 models.

Nonlinear Program Construction and Verification Method Based on Partition Recursion and Morgan's Refinement Rules

The traditional program refinement strategy cannot be refined to an executable program, and there are issues such as low verification reliability and automation. To solve the above problems, this paper proposes a nonlinear program construction and verification method based on partition recursion and Morgan's refinement rules. First, we use recursive definition technique to characterize the initial specification. The specification is then transformed into GCL(Guarded Command Language) programs using loop invariant derivation and Morgan's refinement rules. Furthermore, VCG (Verification Condition Generator) is used in the GCL program to generate the verification condition automatically. The Isabelle theorem prover then validates the GCL program's correctness. Finally, the GCL code generates a C++ executable program automatically via the conversion system. The effectiveness of this method is demonstrated using binary tree preorder traversal program construction and verification as an example. This method addresses the problem that the construction process's loop invariant is difficult to obtain and the refinement process is insufficiently detailed. At the same time, the method improves verification process automation and reduces the manual verification workload.

When Tree Meets Hash: Reducing Random Reads for Index Structures on Persistent Memories

Indexing structures are widely used in modern data-processing applications to support high-performance queries, and there are a variety of recent designs specifically optimized for the newly available persistent memory (PM). The primary focus of previous PM indexes is on reducing the expensive PM writes for persisting data. However, we find that in tree-based PM indexes, because of the smaller performance gap between writes and random reads on real PM devices, the read-intensive tree traversal phase dominates the overall latency. This observation calls for further optimizations on existing indexing structures for PM. In this paper, we propose Extendible Radix Tree (ERT), an efficient indexing structure for PM that significantly reduces tree heights to minimize random reads, while still maintaining fast in-node search speed. The key idea is to use extendible hashing for each node in a radix tree. This design allows us to have a relatively large fanout of the radix tree to keep the tree height small, and also to realize constant-time lookups within a node. Using extendible hashing also allows for incremental node modification without excessive writes during inserts and updates. Range queries are efficiently and robustly handled by enforcing partial ordering among the keys in the hash table of each node without introducing more hash collisions. Our experiments on both synthetic and real-world data sets demonstrate that ERT achieves up to 2.65×, 4.41×, and 2.43× speedups for search, insert, and range queries over the respectively state-of-the-art PM index.

Some New Concepts of Tree Traversal in Binary Tree

Some New Concepts of Tree Traversal in Binary Tree

Sensor Network Design based on the Observability and Precision degree

The Unscented Kalman Filter is a state estimation method used in nonlinear dynamic systems to estimate the mean and covariance of a random variable undergoing a nonlinear transformation, knowing the process model and the measurements. Therefore, an adequate choice of the measured variables improves the performance of the filter technique. In this context, the sensor network design problem allows selecting a set of variables that minimizes the global estimation error when the instrumentation budget is limited. This is solved using a level traversal tree search algorithm, whose computation time is reduced by evaluating the design criteria sequentially. In this work, it is proposed to address the effect of the circumstantial loss of measurements on the system observability and the estimates precision. The success of the sensor network design methodology is demonstrated for the copolymerization process of Methyl Methacrylate and Vinyl Acetate, widely studied in the literature.

SwPHoToNs: Toward trillion‐body‐scale cosmologicalN‐body simulations on SunwayTaihuLightsupercomputer

AbstractCosmologicalN‐body simulations have been essential for astronomers to study the formation of nonlinear structures and hypotheses of dark matter, dark energy, etc. The scale of the problem naturally leads to extreme scenarios with billions or even trillions of particles, thus demanding massive computational power and highly efficient algorithms. In this paper, we present swPHoToNs, a Particle‐Mesh (PM) and Fast Multipole Method‐ (FMM) based code that can perform cosmological simulations with trillions of particles efficiently on the Sunway TaihuLight supercomputer. Our design includes three novel optimizations: (1) a multilevel domain decomposition and dynamic load‐balancing scheme; (2) a pipeline strategy for tree traversal and gravity calculation; (3) optimizations for both computation and MPI kernels with consideration of the hardware features. We manage to conduct cosmological simulations which contain up to 1.6 trillion particles, obtaining a sustained performance of 56.3 PFlops with a weak‐scaling parallel efficiency of 80.9% and a computational efficiency of 44.9%.

Game-Theory-Based Mode Switch Control Schedule Design for Variable Cycle Engine

The variable cycle engine selects the appropriate working mode through mode switch to meet the requirements of low specific fuel consumption and high unit thrust. When the variable cycle engine switches between different modes, it should ensure the smooth transition of working modes and obtain the expected performance at the same time. Consequently, a general control schedule design method for mode switch is investigated in this paper. The feasible switching domains of single-bypass working mode and double-bypass working modes are obtained based on multifurcating tree traversal, and the switching point in the feasible switching domain is determined by solving the collaboration-game optimization problem based on sequential quadratic programming (SQP). Finally, the schedule of control variables is designed to realize smooth and fast switching between different working modes of variable cycle engine. The simulations show that based on the general control schedule of mode switch proposed in this paper, smooth transition of thrust and rotor speed can be achieved under the premise of safe engine operation, with small fluctuations and a short switching time, which is about 2.5 s.

Deep Forest and Pruned Syntax Tree-Based Classification Method for Java Code Vulnerability

The rapid development of J2EE (Java 2 Platform Enterprise Edition) has brought unprecedented severe challenges to vulnerability mining. The current abstract syntax tree-based source code vulnerability classification method does not eliminate irrelevant nodes when processing the abstract syntax tree, resulting in a long training time and overfitting problems. Another problem is that different code structures will be translated to the same sequence of tree nodes when processing abstract syntax trees using depth-first traversal, so in this process, the depth-first algorithm will lead to the loss of semantic structure information which will reduce the accuracy of the model. Aiming at these two problems, we propose a deep forest and pruned syntax tree-based classification method (PSTDF) for Java code vulnerability. First, the breadth-first traversal of the abstract syntax tree obtains the sequence of statement trees, next, pruning statement trees removes irrelevant nodes, then we use a depth-first based encoder to obtain the vector, and finally, we use deep forest as the classifier to get classification results. Experiments on publicly accessible vulnerability datasets show that PSTDF can reduce the loss of semantic structure information and effectively remove the impact of redundant information.

Fast period estimation of X-ray pulsar signals using an improved fast folding algorithm

An accurate period is important to recover the pulse profile from a recorded photon event series of an X-ray pulsar and to estimate the pulse time of arrival, which is the measurement of X-ray pulsar navigation. Epoch folding is a classical period estimation method in the time domain; however, its computational complexity grows as the number of trail periods increases. In order to reduce the computational complexity, this paper improves the fast folding algorithm through segment correlation and amplitude accumulation, which is based on the post-order traversal of a binary tree. Compared with epoch folding, the improved fast folding algorithm can achieve a similar accuracy at the cost of a lower computational burden. Compared with the original fast folding algorithm, the improved algorithm can be applied to detectors with a much smaller effective area. The performance of the method is investigated by simulation data and observation data from the Neutron star Interior Composition Explorer (NICER).

Residency Octree: A Hybrid Approach for Scalable Web-Based Multi-Volume Rendering.

We present a hybrid multi-volume rendering approach based on a novel Residency Octree that combines the advantages of out-of-core volume rendering using page tables with those of standard octrees. Octree approaches work by performing hierarchical tree traversal. However, in octree volume rendering, tree traversal and the selection of data resolution are intrinsically coupled. This makes fine-grained empty-space skipping costly. Page tables, on the other hand, allow access to any cached brick from any resolution. However, they do not offer a clear and efficient strategy for substituting missing high-resolution data with lower-resolution data. We enable flexible mixed-resolution out-of-core multi-volume rendering by decoupling the cache residency of multi-resolution data from a resolution-independent spatial subdivision determined by the tree. Instead of one-to-one node-to-brick correspondences, each residency octree node is mapped to a set of bricks from different resolution levels. This makes it possible to efficiently and adaptively choose and mix resolutions, adapt sampling rates, and compensate for cache misses. At the same time, residency octrees support fine-grained empty-space skipping, independent of the data subdivision used for caching. Finally, to facilitate collaboration and outreach, and to eliminate local data storage, our implementation is a web-based, pure client-side renderer using WebGPU and WebAssembly. Our method is faster than prior approaches and efficient for many data channels with a flexible and adaptive choice of data resolution.

Automatic Extraction Method of Weld Weak Defect Features for Ultra-High Voltage Equipment

To solve the problems of low precision of weak feature extraction, heavy reliance on labor and low efficiency of weak feature extraction in X-ray weld detection image of ultra-high voltage (UHV) equipment key parts, an automatic feature extraction algorithm is proposed. Firstly, the original weld image is denoised while retaining the characteristic information of weak defects by the proposed monostable stochastic resonance method. Then, binarization is achieved by combining Laplacian edge detection and Otsu threshold segmentation. Finally, the automatic identification of weld defect area is realized based on the sequential traversal of binary tree. Several characteristic analysis dimensions are established for weld defects of UHV key parts, including defect area, perimeter, slenderness ratio, duty cycle, etc. The experiment using the weld detection image of the actual production site shows that the proposed method can effectively extract the weak feature information of weld defects and further provide reference for decision-making.

A Simple Lossless Algorithm for On-Board Satellite Hyperspectral Data Compression

As resolution of on-board imaging spectrometer keeps improving, data acquisition rate increases and resource limited satellite environment necessitates for computationally simple data compression methods to meet timing, bandwidth and resource requirements with error resilience. This letter proposes a new lossless, prediction based algorithm for on-board satellite hyperspectral data compression that utilizes spectral as well as spatial correlation and at the same time, is computationally less complex. Concept of non-binary tree traversal is used with nearest neighbor method and implemented using neighbor driven decision making in pre-processing stage. Previously processed pixels are used to minimize the prediction residual, which makes more than 80% calculations causal in nature and thereby reducing the computational complexity of the algorithm. The prediction residual is then encoded using sample adaptive Golomb coding in band-sequential order. CCSDS corpus of data for hyperspectral images is used for evaluating the performance of the algorithm. The proposed method shows reduced computational complexity and lesser data dependencies compared to the CCSDS 123.0-B-1 standard when similar spectral vicinity is considered, and comparable compression performance compared to other state-of-the-art on-board lossless compression methods.

Improved Differential and Linear Trail Bounds for ASCON

Ascon is a family of cryptographic primitives for authenticated encryption and hashing introduced in 2015. It is selected as one of the ten finalists in the NIST Lightweight Cryptography competition. Since its introduction, Ascon has been extensively cryptanalyzed, and the results of these analyses can indicate the good resistance of this family of cryptographic primitives against known attacks, like differential and linear cryptanalysis.Proving upper bounds for the differential probability of differential trails and for the squared correlation of linear trails is a standard requirement to evaluate the security of cryptographic primitives. It can be done analytically for some primitives like AES. For other primitives, computer assistance is required to prove strong upper bounds for differential and linear trails. Computer-aided tools can be classified into two categories: tools based on general-purpose solvers and dedicated tools. General-purpose solvers such as SAT and MILP are widely used to prove these bounds, however they seem to have lower capabilities and thus yield less powerful bounds compared to dedicated tools.In this work, we present a dedicated tool for trail search in Ascon. We arrange 2-round trails in a tree and traverse this tree in an efficient way using a number of new techniques we introduce. Then we extend these trails to more rounds, where we also use the tree traversal technique to do it efficiently. This allows us to scan much larger spaces of trails faster than the previous methods using general-purpose solvers. As a result, we prove tight bounds for 3-rounds linear trails, and for both differential and linear trails, we improve the existing upper bounds for other number of rounds. In particular, for the first time, we prove bounds beyond 2−128 for 6 rounds and beyond 2−256 for 12 rounds of both differential and linear trails.

FPGA-Based Updatable Packet Classification Using TSS-Combined Bit-Selecting Tree

OpenFlow switches are being deployed in SDN to enable a wide spectrum of non-traditional applications. As a promising alternative to brutal force TCAMs, FPGA-based packet classification is being actively investigated. However, none of the existing FPGA designs can achieve high performance on both search and update for large-scale rule sets. To address this issue, we propose TcbTree, an FPGA-based algorithmic scheme for packet classification. Specifically, at the algorithmic side, i) a two-stage framework consisting of heterogeneous algorithms is proposed, where most rules can be mapped into several balanced trees without rule replications, ii) for the remaining few rules, a centralized TSS (Tuple Space Search) architecture together with a real-time feedback scheme is designed to enhance the efficiency of TSS search on FPGA, and iii) a tree dilution method is designed to equalize rule distribution in trees, so that the latency of tree search can be reduced. At the hardware side, i) an efficient data structure set is designed to convert tree traversal to addressing process, which breaks the constraints of limited tree depth and imbalanced node distribution, and ii) distinct from fully pipelined designs, multiple levels of parallelism are efficiently explored with multi-core, multi-search-engine and coarse-grained pipelines herein. Experimental results using ClassBench show that, with the implementation of TcbTree on FPGA, the average classification throughputs for 1k, 10k, 32k and 100k rule sets achieve 788.8 MPPS, 404.3 MPPS, 237 MPPS and 41.8 MPPS, respectively, and the update throughput for all benchmark rule sets is above 1 MUPS.

A tree-structure-guided graph convolutional network with contrastive learning for the assessment of parkinsonian hand movements.

Bradykinesia is one of the core motor symptoms of Parkinson's disease (PD). Neurologists typically perform face-to-face bradykinesia assessment in PD patients according to the Movement Disorder Society-sponsored revision of the Unified Parkinson's Disease Rating Scale (MDS-UPDRS). As this human-expert assessment lacks objectivity and consistency, an automated and objective assessment scheme for bradykinesia is critically needed. In this paper, we propose a tree-structure-guided graph convolutional network with contrastive learning scheme to solve the challenge of difficulty in fine-grained feature extraction and insufficient model stability, finally achieving the video-based automated assessment of Parkinsonian hand movements, which represent a vital MDS-UPDRS component for examining upper-limb bradykinesia. Specifically, a tri-directional skeleton tree scheme is proposed to achieve effective fine-grained modeling of spatial hand dependencies. In this scheme, hand skeletons are extracted from videos, and then the spatial structures of these skeletons are constructed through depth-first tree traversal. Afterwards, a tree max-pooling module is employed to establish remote exchange between outer and inner nodes, hierarchically gather the most salient motion features, and hence achieve fine-grained mining. Finally, a group-sparsity-induced momentum contrast is also developed to learn similar motion patterns under different interference through contrastive learning. This can promote stable learning of discriminative spatial-temporal features with invariant motion semantics. Comprehensive experiments on a large clinical video dataset reveal that our method achieves competitive results, and outperforms other sensor-based and RGB-depth methods. The proposed method leads to accurate assessment of PD bradykinesia through videos collected by low-cost consumer cameras of limited capabilities. Hence, our work provides a convenient tool for PD telemedicine applications with modest hardware requirements.

TABI-PB 2.0: An Improved Version of the Treecode-Accelerated Boundary Integral Poisson-Boltzmann Solver.

This work describes TABI-PB 2.0, an improved version of the treecode-accelerated boundary integral Poisson-Boltzmann solver. The code computes the electrostatic potential on the molecular surface of a solvated biomolecule, and further processing yields the electrostatic solvation energy. The new implementation utilizes the NanoShaper surface triangulation code, node-patch boundary integral discretization, a block preconditioner, and a fast multipole method based on barycentric Lagrange interpolation and dual tree traversal. Performance-critical portions of the code were implemented on a GPU. Numerical results for protein 1A63 and two viral capsids (Zika, H1N1) demonstrate the code's accuracy and efficiency.

Symmetric Encryption using Artificial Neural Network, Binary Tree Traversal, and Interleaving Salting

We have proposed a novel way of symmetric encryption utilizing interleaving salting, Binary Tree traversal, and an Artificial Neural Network in a sequential manner. We have presented the use of an Artificial Neural Network as an invertible(reversible) mathematical function so that decryption of the encrypted output may be possible. Knowledge of the encryption pipeline, salt, and neural network weights is required for decryption. As the same set of values is required for encryption and decryption, our proposed approach is a type of symmetric-key algorithm. Each user will have a unique key. Thus if a key attributing to a particular user is compromised, the integrity of the data of the remaining users will still be maintained. Our approach can be utilized to encrypt text data such as messages, documents, and letters. The encryption process consists of interleaving salting, creation of binary tree by considering the input as its level order traversal, and passing the preorder and inorder traversal of the constructed binary tree as input to the Artificial Neural Network. The output of the Artificial Neural Network would be the encrypted data. Decryption would require determining the input of an Artificial Neural Network from the output, hence solving multiple sets of linear equations and constructing a binary tree from its preorder and inorder traversal. We have then analyzed the variation of performance with the change in the input string size. The codebase of our proposed approach is publicly available at https://github.com/Atishaysjain/Symmetric-Encryption-using-ANN-and-Binary-Trees.