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20th International Carpathian Control Conference (ICCC)

作者： Kvet, Marek Univ Zilina Fac Management Sci & Informat Univ 8215-1 Zilina 01026 Slovakia

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.

关键词： Rescue system Robustness Radial formulation approximate algorithm

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An approximate algorithm to Solve Facility Layout Problem

An Approximate Algorithm to Solve Facility Layout Problem

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IEEE International Advance Computing Conference

作者： Singh, S. P. Xavier Inst Management Bhubaneswar Dept Operat Management & Decis Sci Bhubaneswar Orissa India

ISBN: (纸本)9781424429271

In this paper, an approximate algorithm is proposed to solve facility layout problem (FLP) which is formulated as quadratic assignment problem (QAP). In the proposed approach, linear assignment problem (LAP) is formulated which is solvable in polynomial time. The proposed heuristic is applied to solve FLP from the set of LAP solution. To evaluate the performance of the heuristic a comparison between optimal and heuristic solution is also provided. The approach is tested on numerous benchmark problems available in literature. An encouraging comparative performance of this procedure is thus reported.

关键词： facility layout problem QAP approximate algorithm linear programming

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An approximate algorithm for the Chromatic Number of Graphs

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Electronic Notes in Discrete Mathematics 2014年第1期46卷 89-96页

作者： de Ita Luna, Guillermo Raymundo Marcial-Romero, J. Moyao, Yolanda Facultad de Ciencias de la Computación BUAP Puebla Mexico Facultad de Ingeniería UAEMex Toluca Mexico

We have designed a novel polynomial-time approximate algorithm for the graph vertex colouring problem. Contrary to the common top-down strategy for solving the colouring graph problem, we propose a bottom-up algorithm for colouring graphs. Given an input graph G, we establish an upper bound to approximate the colouring of the input grap given by ⌈δ(G)/2⌉. +. 2 where δ(G) is the average degree of G. © 2014 Elsevier B.V.

关键词： approximate algorithm Chromatic Number Graph Coloring

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A real space convolution-based approximate algorithm for phase field model involving elastic strain energy

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NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS 2024年第6期40卷

作者： Gao, YaQian Chi, XueBin Yin, JiXian Zhang, Jian Chinese Acad Sci Comp Network Informat Ctr Beijing Peoples R China Univ Chinese Acad Sci Beijing Peoples R China

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.

关键词： approximate algorithm elastic strain energy large-scale simulation phase field model

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2-approximate algorithm for Touring a Sequence of Pairwise Disjoint Simple Polygons

2-Approximate Algorithm for Touring a Sequence of Pairwise D...

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2017 2nd International Conference on Computational Modeling, Simulation and Applied Mathematics（CMSAM 2017)

作者： Shun LYU Bo JIANG Dalian Maritime University

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.

关键词： Computational geometry Touring polygons problem approximate algorithm Simple polygon Ratio

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Simpler Minimum Enclosing Ball: Fast approximate MEB algorithm for Extensive Kernel Methods

Simpler Minimum Enclosing Ball: Fast Approximate MEB Algorit...

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20th Chinese Control and Decision Conference

作者： Wang, Yongqing Zou, Yongkang Zheng, Suiwu Guo, Xinlan Chinese Acad Sci Inst Automat Beijing 100080 Peoples R China Chongqing Univ Arts & Sci Dept Math & Comp Sci Chongqing 402160 Peoples R China

ISBN: (纸本)9781424417339

We develop a simple and fast (1 + is an element of)-approximate algorithm for computing the Minimum Enclosing Ball (MEB) of a points set in high dimensional Euclidean space without requirement of any numerical solver. We prove theoretically that the proposed Simpler Minimum Enclosing Ball (SMEB) algorithm converges to the optimum within any precision in O(1/is an element of) iterations. Compared to the MEB algorithms adopted in the Core Vector Machines (CVM) and Simpler Core Vector Machines (SCVM) recently arisen, it has the competitive performances in both training time and accuracy. Besides, the proposed algorithm does not need any extra requirement of kernels, it can be linked with extensive kernel methods, consequently. We also present the potential application areas for the algorithm theoretically, such as Unbalanced SVM and Ranking SVM. Experiments demonstrate the validity of the algorithm we proposed.

关键词： Kernel methods support vector machines minimum enclosing ball approximate algorithm

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Exact and approximate computation of the scatter halfspace depth

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COMPUTATIONAL STATISTICS 2025年第1期40卷 547-572页

作者： Liu, Xiaohui Liu, Yuzi Laketa, Petra Nagy, Stanislav Chen, Yuting Jiangxi Univ Finance & Econ Sch Stat Nanchang 330013 Jiangxi Peoples R China Charles Univ Prague Fac Math & Phys Prague 18675 Czech Republic Univ Maryland Joint Program Survey Methodol College Pk MD 20742 USA

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.

关键词： Scatter halfspace depth Depth Exact computation approximate algorithm

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approximate algorithms for document placement in distributed Web servers

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IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 2005年第6期16卷 489-496页

作者： Tse, SSH Univ Hong Kong Dept Comp Sci Hong Kong Hong Kong Peoples R China

We study approximate algorithms for placing a set of documents into M distributed Web servers in this paper. We define the load of a server to be the summation of loads induced by all documents stored. The size of a server is defined in a similar manner. We propose five algorithms. algorithm 1 balances the loads and sizes of the servers by limiting the loads to k(l) and the sizes to k(s) times their optimal values, where 1/k(l)-1 + 1/k(s)-1 <= 1. This result improves the bounds on load and size of servers in [ 10]. algorithm 2 further reduces the load bound on each server by using partial document replication, and algorithm 3 by sorting. algorithm 4 employs both partial replication and sorting. Last, without using sorting and replication, we give algorithm 5 for the dynamic placement at the cost of a factor O(log M) in the time-complexity.

关键词： distributed Web server load balancing document placement document replication file allocation problem approximate algorithm NP-completeness

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Towards cost optimization in security-aware service function chaining and embedding over multi-vendor edge networks

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COMPUTER NETWORKS 2025年 257卷

作者： Wang, Chao Zheng, Danyang Liu, Xiaorong Tang, Wenyi Xu, Honghui Cao, Xiaojun Southwest Jiaotong Univ Sch Comp & Artificial Intelligence Chengdu Peoples R China Sichuan Univ Sch Cyber Sci & Engn Chengdu Peoples R China Kennesaw State Univ Dept Informat Technol Kennesaw GA USA Georgia State Univ Dept Comp Sci Atlanta GA USA

Frequent cyber-attacks compel service providers to employ security-aware service functions (S-SFs) while delivering network services. Typically, one S-SF can be implemented by diverse configurations, each requiring different implementation costs and providing various security levels. These multi-configured S-SFs could compose various security-aware service function chains (S-SFCs) to satisfy the security requirement of incoming network request. How to properly compose an S-SFC and effectively deploy it remains an open challenging problem. In this work, we discover the "reDundancy security A ccumulatio N "(DAN) phenomenon caused by the direct-summation-fashion when calculating the security level (SeL) of an S-SFC and propose novel methodology to estimate the SeL of one S-SFC for avoiding DAN. To begin, we introduce the concept security level indicator (SeLI) and our novel methodology. Next, we formulate the problem of security-aware SF selection, chaining, and deployment (Sec-SFCD) with the objective function of cost optimization and prove its NP-hardness. To solve this problem, we propose the security-cost-balance (SCB) factor technique, which measures the average cost of satisfying one unit of security requirement. Based on this technique, we further develop an efficient algorithm called SCB-based S-SFC deployment (SCB-SD) and improves it by proposing overflowing security level elimination (OSE) technique. Through our thorough analysis, we show the logarithm approximation of SCB-SD and SCB-SD with OSE technique (SSD-OSE). The extensive simulation results validate SSD-OSE' s logarithm-approximation and demonstrate that it significantly outperforms the benchmarks directly extended from the state-of-the-art by an average of 17.98 % and 67.47 %.

关键词： Security-aware service function chain Security level estimation approximate algorithm Cost optimization

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Improving density peak clustering on multi-dimensional time series: rediscover and subdivide

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KNOWLEDGE AND INFORMATION SYSTEMS 2025年第2期67卷 1573-1596页

作者： Wang, Huina Liu, Bo Zhao, Huaipu Qu, Guangzhi Beijing Univ Technol Fac Informat Technol Sch Software Engn Beijing 100124 Peoples R China Massey Univ Sch Math & Computat Sci Auckland 0745 New Zealand Oakland Univ Comp Sci & Engn Dept Rochester MI 48309 USA

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.

关键词： Density peak clustering approximate algorithm Multi-dimensional time series Nearest neighbor

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