Phase field models have been employed extensively in the study of microstructure evolution in materials. Elasticity plays an important role in solid-state phase transformation processes, and it is usually introduced i...
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Phase field models have been employed extensively in the study of microstructure evolution in materials. Elasticity plays an important role in solid-state phase transformation processes, and it is usually introduced into phase field models in terms of the elastic strain energy by applying Khachaturyan-Shatalov microelasticity theory. Conventionally, this energy is derived in the reciprocal space and results in full-space Fourier transformation in practice, which becomes bottle-neck in large-scale and massively-parallel applications. In this article, we propose an error-controlled approximation algorithm for scalable and efficient calculation of the elastic strain energy in phase field models. We first derive a real-space convolutional representation of the elastic strain energy by representing the equilibrium displacements in the Khachaturyan-Shatalov microelasticity theory using Green's function. Then we propose an error-controlled truncation criterion to approximate the corresponding terms in the phase field model. Finally, a carefully designed parallel algorithm is presented to carry out large-scale simulations. The accuracy and efficiency of the proposed algorithm are demonstrated by real-world large-scale phase field simulations.
In the era of big data,correlation analysis is significant because it can quickly detect the correlation between *** then,it has been received much *** to the good properties of generality and equitability of the maxi...
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In the era of big data,correlation analysis is significant because it can quickly detect the correlation between *** then,it has been received much *** to the good properties of generality and equitability of the maximal information coefficient(MIC),MIC is a hotspot in the research of correlation ***,if the original approximate algorithm of MIC is directly applied into mining correlations in big data,the computation time is very *** the theoretical time complexity of the original approximate algorithm is analyzed in depth and the time complexity is n2.4 when parameters are *** the experiments show that the large number of candidate partitions of random relationships results in long computation *** analysis is a good preparation for the next step work of designing new fast algorithms.
This contribution is aimed at advanced rescue system designing. Since the modelled decisions are strategic and often have a long-term impact on accessibility and effectiveness of service providing, several aspects sho...
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ISBN:
(纸本)9781728107011
This contribution is aimed at advanced rescue system designing. Since the modelled decisions are strategic and often have a long-term impact on accessibility and effectiveness of service providing, several aspects should be taken into account when a integer-programming model of the problem is created. One of them consists in system robustness that means its resistance to randomly occurring failures in the associated transportation network, which is used by ambulance vehicles when delivering rescue service to system users. To incorporate system robustness into the particular integer-programming model, a finite set of failure scenarios is usually formed. Then, the optimal robust rescue system design can be obtained by minimization of the highest detrimental impact of the individual scenarios. A simple rescue system design can be modelled as a weighted p-median problem. While a weighted p-median problem is easily solvable, the robust system design often causes computational difficulties due to the model size and its complicated structure. Therefore, the main goal of this contribution is to develop a fast algorithm for robust rescue system design, which enables to obtain a good approximate solution of the original problem in a short time. The theoretical explanation is here accompanied by a computational study.
In this paper, a 2-approximate algorithm is described to answer the previously open problem "What is the complexity of the TPP for disjoint non-convex simple polygons" which is known to NP-hard. We provide a...
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In this paper, a 2-approximate algorithm is described to answer the previously open problem "What is the complexity of the TPP for disjoint non-convex simple polygons" which is known to NP-hard. We provide a O(kn) approximate algorithm, where k is polygon counts, and n is the number of vertexes of the polygons, to efficiently find a path which is 2 times at most than the shortest path. To solve this problem, we transform all of simple polygons into corresponding convex polygons, then process the shortest path of convex polygons according to the parity of polygons sequence and finally obtain the approximate path of simple polygons.
Connectivity problems are among the most challenging issues in Mobile Wireless Sensor Networks (MWSNs). Ensuring connectivity in such networks means finding network configurations in which all mobile sensors can conne...
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Connectivity problems are among the most challenging issues in Mobile Wireless Sensor Networks (MWSNs). Ensuring connectivity in such networks means finding network configurations in which all mobile sensors can connect to a base station during data gathering events. This paper considers MWSNs in which a minimal number of relay nodes need to be placed in order to maintain connectivity. Two algorithms are proposed: AST (Approximation Steiner Tree) is an approximate algorithm with a ratio of 2 x opt + O(K x N) (where K x N is the number of nodes on the time-flattened domain) and CBAST (Cluster-Based on the Approximation Steiner Tree algorithm) is a highly effective heuristic. Both algorithms focus on optimal Steiner Tree construction to produce high-quality solutions. AST is an approximation based on 3-point Steiner Trees, while CBAST forms clusters of static components and uses a 2-approximation algorithm to maintain connectivity in each cluster. Experiments on a large number of generated instances are performed to compare AST and CBAST with existing state-of-the-art heuristics. Our results show that CBAST significantly outperforms baseline methods while also reducing computation time and energy consumption.
The scatter halfspace depth (sHD) is an extension of the location halfspace (also called Tukey) depth that is applicable in the nonparametric analysis of scatter. Using sHD, it is possible to define minimax optimal ro...
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The scatter halfspace depth (sHD) is an extension of the location halfspace (also called Tukey) depth that is applicable in the nonparametric analysis of scatter. Using sHD, it is possible to define minimax optimal robust scatter estimators for multivariate data. The problem of exact computation of sHD for data of dimension d >= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d \ge 2$$\end{document} has, however, not been addressed in the literature. We develop an exact algorithm for the computation of sHD in any dimension d and implement it efficiently for any dimension d >= 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d \ge 1$$\end{document}. Since the exact computation of sHD is slow especially for higher dimensions, we also propose two fast approximate algorithms. All our programs are freely available in the R package scatterdepth.
Graphs (networks) are an important tool to model data in different domains. Real-world graphs are usually directed, where the edges have a direction and they are not symmetric. Betweenness centrality is an important i...
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Graphs (networks) are an important tool to model data in different domains. Real-world graphs are usually directed, where the edges have a direction and they are not symmetric. Betweenness centrality is an important index widely used to analyze networks. In this paper, first given a directed network G and a vertex r is an element of V(G), we propose an exact algorithm to compute betweenness score of r. Our algorithm pre-computes a set RV(r), which is used to prune a huge amount of computations that do not contribute to the betweenness score of r. Time complexity of our algorithm depends on vertical bar RV(r)vertical bar and it is respectively Theta(vertical bar RV(r)vertical bar . vertical bar E(G)vertical bar) and Theta(vertical bar RV(r)vertical bar . vertical bar E(G)vertical bar + vertical bar RV(r)vertical bar . vertical bar V (G)vertical bar log vertical bar V (G)vertical bar) for unweighted graphs and weighted graphs with positive weights. jRV(r)j is bounded from above by vertical bar V (G)vertical bar - 1 and in most cases, it is a small constant. Then, for the cases where RV(r) is large, we present a simple randomized algorithm that samples from RV(r) and performs computations for only the sampled elements. We show that this algorithm provides an (epsilon, delta)-approximation to the betweenness score of r. Finally, we perform extensive experiments over several real-world datasets from different domains for several randomly chosen vertices as well as for the vertices with the highest betweenness scores. Our experiments reveal that for estimating betweenness score of a single vertex, our algorithm significantly outperforms the most efficient existing randomized algorithms, in terms of both running time and accuracy. Our experiments also reveal that our algorithm improves the existing algorithms when someone is interested in computing betweenness values of the vertices in a set whose cardinality is very small.
Bipartite graph models the relationship between two different sets of entities. Such graph data become more dynamic and are organized as stream with duplicate edges in real-word applications such as customer-product i...
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ISBN:
(纸本)9798400704369
Bipartite graph models the relationship between two different sets of entities. Such graph data become more dynamic and are organized as stream with duplicate edges in real-word applications such as customer-product in e-commerce. A butterfly, (2,2)-biclique, is the simplest cohesive substructure and of great importance in a bipartite graph. However, it is challenging to estimate the number of butterflies in large scale and high dynamic bipartite graph stream when given a limited memory. Besides, existing works for butterfly counting assume no duplicate edges in the bipartite graph stream, which cause less accuracy in bipartite graph stream with duplicate edges. In this paper, we propose FABLE, a Fixed-size memory approximate Butterfly counting algorithm for dupLicate Edges in bipartite graph stream. In FABLE, we compute the number of distinct edges by maintaining an ordered list of edge priorities for replacement and sampling. We provide theoretical proof of unbiasedness and derive the variance of butterfly count. Our extensive experiments on 5 real-world datasets confirm that our approach has higher accuracy compared with the baseline method under the same memory usage.
The density peak clustering (DPC) algorithm identifies patterns in high-dimensional data and obtains robust outcomes across diverse data types with minimal hyperparameters. However, DPC may produce inaccurate pattern ...
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The density peak clustering (DPC) algorithm identifies patterns in high-dimensional data and obtains robust outcomes across diverse data types with minimal hyperparameters. However, DPC may produce inaccurate pattern sizes in multi-dimensional datasets and exhibit poor performance in recognizing similar patterns. To solve these issues, we propose the rediscover and subdivide density peak clustering algorithm (RSDPC), which follows three key strategies. The first strategy, rediscover, iteratively uncovers prominent patterns within the existing data. The second strategy, subdivide, partitions patterns into several similar subclasses. The third strategy, re-sort, rectifies errors from the preceding steps by incorporating critical distance and nearest distance considerations. The experimental results show that RSDPC is feasible and effective in synthetic and practical datasets compared with state-of-the-art works.
Access control policy mining, which extracts or infers access control policies from existing system logs or configurations within a given environment, is widely applied in policy migration. No policy mining algorithm ...
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Access control policy mining, which extracts or infers access control policies from existing system logs or configurations within a given environment, is widely applied in policy migration. No policy mining algorithm can produce completely accurate policies, necessitating human intervention to correct errors before implementation. However, humans may fail to revise the produced policies without fully understanding all permission details. In this paper, we propose an on-the-fly framework to assist human revisions by mining usable policies. This framework is formulated as an approximate optimization problem, designed to avoid permission errors and redundancy by balancing submodularity and modular costs through an iterative search for access rules. The search space is guided by two pruning techniques: a tight optimistic estimate to only eliminate unpromising candidates and a queue cutter to sample promising candidates in advance. Experimental evaluations on two real-world and three publicly available synthetic datasets indicate that: 1) our method produces more concise results than existing methods, achieving a 93.2% reduction in redundancy;2) our method is at least five times faster than state-of-the-art approaches. To further validate the usability of the policies obtained by our approach, we conducted a user study involving 30 participants and 7 large language models (LLMs). The results show that 90.9% of participants, including LLMs such as gpt-4o-mini, successfully modified our mined policies to meet given permission goals.
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