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Preference based multi-issue negotiation algorithm (PMINA) for fog resource allocation 用于雾资源分配的基于偏好的多问题协商算法(PMINA)
IF 3.7 3区 计算机科学 Q2 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-03-09 DOI: 10.1007/s00607-024-01271-4
Shaifali Malukani, C. K. Bhensdadia

Fog computing has emerged as a decentralized computing paradigm that extends cloud services to the network edge, enabling faster data processing and real-time applications. The increasing popularity of fog computing has led to the emergence of a potential market involving users and providers of fog resources. However, both parties are driven by self-interest and seek to maximize their utility, giving rise to multiple conflicts extending beyond mere price considerations. Negotiations can play a crucial role in resolving conflicts and establishing mutually beneficial service level agreements. Moreover, in the heterogeneous fog environment, quality of service attributes, such as throughput, delay, trust, power dissipation, etc., vary significantly among different user-fog associations. These attributes, although non-negotiable, hold great importance for entities and directly influence partner selection. Entities may exhibit a preference for one another based on these non-negotiable attributes. To the best of our knowledge, no existing literature specifically addresses the issue of associating with a preferred trading partner at a negotiated value for multiple issues in the fog environment. This research aims to address this gap and provide insights into this unexplored area. This work presents a novel Preference-based Muti-Issue Negotiation Algorithm, PMINA, for many to many, bilateral and concurrent negotiations in the fog environment. The results confirm the significance of PMINA, demonstrating a substantial enhancement in user and fog utilities.

雾计算是一种分散式计算模式,可将云服务扩展到网络边缘,实现更快的数据处理和实时应用。随着雾计算的日益普及,出现了一个涉及雾资源用户和提供商的潜在市场。然而,双方都受到自身利益的驱使,都在寻求自身效用的最大化,这就引发了多种冲突,而不仅仅是价格方面的考虑。谈判在解决冲突和建立互惠互利的服务水平协议方面可以发挥至关重要的作用。此外,在异构雾环境中,服务质量属性(如吞吐量、延迟、信任、功率耗散等)在不同的用户-雾关联中差异很大。这些属性虽然不可协商,但对实体非常重要,并直接影响合作伙伴的选择。实体可能会根据这些不可协商的属性表现出对彼此的偏好。据我们所知,目前还没有任何文献专门论述在雾环境中就多个问题以协商值与首选贸易伙伴建立联系的问题。本研究旨在填补这一空白,并为这一尚未探索的领域提供见解。本研究提出了一种新颖的基于偏好的多问题谈判算法(PMINA),适用于雾环境中的多对多、双边和并发谈判。研究结果证实了 PMINA 的重要意义,表明它大大提高了用户和雾的效用。
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引用次数: 0
Time-sensitive propagation values discount centrality measure 时间敏感传播值折扣中心度量
IF 3.7 3区 计算机科学 Q2 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-03-04 DOI: 10.1007/s00607-024-01265-2

Abstract

The detection of influential individuals in social networks is called influence maximization which has many applications in advertising and marketing. Several factors including propagation delay affect the degree to which an individual influences the network. Many different methods, including centrality measures, identify high-influence individuals in social networks. The time-sensitive harmonic method (TSHarmonic), which considers time sensitivity to propagation delay and duration, is a centrality measure. TSHarmonic has two weaknesses: high computational complexity and ignoring the influence of the selected node in selecting other influential nodes. Therefore, in this article, the valuable path-finding process in the TSHarmonic method is modified to provide the Fast Time-Sensitive Harmonic algorithm. The provided method has the same accuracy as the TSHarmonic, while the speed is significantly increased. Then, the Time-Sensitive Propagation Values Discount method is proposed to improve detection speed and accuracy. This method takes into account the influence of the selected node for future selection and hence increases the accuracy.

摘要 在社交网络中发现有影响力的个体被称为影响力最大化,它在广告和市场营销中有很多应用。包括传播延迟在内的一些因素会影响个人对网络的影响程度。包括中心度测量在内的许多不同方法都能识别社交网络中的高影响力个体。时间敏感谐波法(TSHarmonic)是一种中心度测量方法,它考虑了传播延迟和持续时间的时间敏感性。TSHarmonic 有两个缺点:计算复杂度高,以及在选择其他有影响力的节点时忽略了所选节点的影响力。因此,本文对 TSHarmonic 方法中有价值的寻路过程进行了修改,提供了快速时敏谐波算法。所提供的方法与 TSHarmonic 方法具有相同的精度,但速度明显提高。然后,提出了时敏传播价值折扣法,以提高检测速度和精度。该方法考虑了所选节点对未来选择的影响,从而提高了准确性。
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引用次数: 0
Cloud data center cost management using virtual machine consolidation with an improved artificial feeding birds algorithm 使用改进型人工饲养鸟算法整合虚拟机的云数据中心成本管理
IF 3.7 3区 计算机科学 Q2 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-03-02 DOI: 10.1007/s00607-024-01267-0
Mohammad Ali Monshizadeh Naeen, Hamid Reza Ghaffari, Hossein Monshizadeh Naeen

Cloud data centers face various challenges, such as high energy consumption, environmental impact, and quality of service (QoS) requirements. Dynamic virtual machine (VM) consolidation is an effective approach to address these challenges, but it is a complex optimization problem that involves trade-offs between energy efficiency and QoS satisfaction. Moreover, the workload patterns in cloud data centers are often non-stationary and unpredictable, which makes it difficult to model them. In this paper, we propose a new method for dynamic VM consolidation that optimizes both energy efficiency and QoS objectives. Our approach is based on Markov chains and the artificial feeding birds (AFB) algorithm. Markov chains are used to model the resource utilization of each individual VM and PM based on the changes that happen in workload data. AFB algorithm is a metaheuristic optimization technique that mimics the behavior of birds in nature. We modify the AFB algorithm to suit the characteristics of the VM placement problem and to provide QoS-aware and energy-efficient solutions. Our approach also employs an online step detection method to capture variations in workload patterns. Furthermore, we introduce a new policy for VM selection from overloaded hosts, which considers the abrupt changes in the utilization processes of the VMs. The proposed algorithms are evaluated extensively using the CloudSim Toolkit with real workload data. The proposed system outperforms evaluation policies in multiple metrics, including energy consumption, SLA violations, and other essential metrics.

云数据中心面临着各种挑战,如高能耗、环境影响和服务质量(QoS)要求。动态虚拟机(VM)整合是应对这些挑战的有效方法,但它是一个复杂的优化问题,涉及能源效率和 QoS 满足之间的权衡。此外,云数据中心的工作负载模式通常是非稳定和不可预测的,这给建模带来了困难。在本文中,我们提出了一种能同时优化能效和 QoS 目标的动态虚拟机整合新方法。我们的方法基于马尔可夫链和人工喂食鸟(AFB)算法。马尔可夫链用于模拟每个虚拟机的资源利用率,并根据工作负载数据的变化进行调整。AFB 算法是一种模仿自然界鸟类行为的元启发式优化技术。我们对 AFB 算法进行了修改,以适应虚拟机放置问题的特点,并提供具有服务质量意识和高能效的解决方案。我们的方法还采用了在线阶跃检测方法,以捕捉工作负载模式的变化。此外,我们还引入了一种从超载主机中选择虚拟机的新策略,该策略考虑了虚拟机利用过程中的突然变化。我们使用云模拟工具包(CloudSim Toolkit)的真实工作负载数据对所提出的算法进行了广泛评估。所提出的系统在多个指标(包括能耗、违反服务水平协议和其他重要指标)上都优于评估策略。
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引用次数: 0
Many-BSP: an analytical performance model for CUDA kernels Many-BSP:CUDA 内核的性能分析模型
IF 3.7 3区 计算机科学 Q2 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-02-26 DOI: 10.1007/s00607-023-01255-w
Ali Riahi, Abdorreza Savadi, Mahmoud Naghibzadeh

The unknown behavior of GPUs and the differing characteristics among their generations present a serious challenge in the analysis and optimization of programs in these processors. As a result, performance models have been developed to better analyze and describe the behavior of these processors. These models help programmers to configure applications and developers to improve the performance of these devices. This paper introduces an analytical model, called Many-BSP, to predict the execution time of a CUDA kernel. This model has high portability and can easily be used on various devices. There are many GPU features and behaviors that affect performance and will be discussed, including multi-threading, coalesced access to global memory, shared memory bank conflict, dual-issue instructions, limitation of functional units, parallelism in instruction, thread and warp levels, the instruction pipeline, branch divergence, and intra-block and inter-block overlapping between communications and computations. This model also employs the tree hierarchy and parameters of the Multi-BSP model to estimate the communication latency with memory. In Many-BSP, the execution time of a kernel is predicted by static analysis of CUDA and PTX codes. The performance of the model is tested on three devices of different generations and three real-world benchmarks. The results show that the execution time of a CUDA kernel can be predicted with a maximum error of 12.33%.

GPU 的未知行为以及各代 GPU 之间的不同特性给分析和优化这些处理器中的程序带来了严峻的挑战。因此,人们开发了性能模型来更好地分析和描述这些处理器的行为。这些模型有助于程序员配置应用程序,也有助于开发人员提高这些设备的性能。本文介绍了一种名为 Many-BSP 的分析模型,用于预测 CUDA 内核的执行时间。该模型具有很高的可移植性,可轻松用于各种设备。我们将讨论影响性能的许多 GPU 特性和行为,包括多线程、全局内存的聚合访问、共享内存库冲突、双发指令、功能单元限制、指令、线程和经线级的并行性、指令流水线、分支发散以及通信和计算之间的块内和块间重叠。该模型还采用多-BSP 模型的树状层次结构和参数来估算与内存的通信延迟。在 Many-BSP 模型中,通过对 CUDA 和 PTX 代码进行静态分析来预测内核的执行时间。该模型的性能在三个不同世代的设备和三个实际基准上进行了测试。结果表明,CUDA 内核的执行时间可以预测,最大误差为 12.33%。
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引用次数: 0
Electricity-cost-aware multi-workflow scheduling in heterogeneous cloud 异构云中的电力成本感知多工作流调度
IF 3.7 3区 计算机科学 Q2 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-02-24 DOI: 10.1007/s00607-024-01264-3
Shuang Wang, Yibing Duan, Yamin Lei, Peng Du, Yamin Wang

Multi-workflows are commonly deployed on cloud platforms to achieve efficient computational power. Diverse task configuration requirements, the heterogeneous nature and dynamic electricity price of cloud servers impose significant challenges for economically scheduling multi-workflows. In this paper, we propose a Heuristic Electricity-cost-aware Multi-workflow Scheduling algorithm (HEMS) to search for an optimal scheduling plan which determines the optimal scheduling scheme for each task in each workflow, specifying the server to perform the task with determined resources in specific time. The objective is to minimize the total electricity cost of all servers while satisfying the deadline constraints of all workflows. The HEMS algorithm consists of five components: Workflow Scheduling Sequence Generation, Task Scheduling Sequence Initialization for each workflow, Optimal Scheduling Scheme Determination for each task, initial Task Scheduling Sequence Optimization, and Optimal Scheduling Plan Optimization. Experimental results demonstrate that HEMS consistently achieves the optimal scheduling plan with the lower total electricity cost (saving 54.5–69.1% on average) within slightly longer CPU time for various multi-workflows compared to existing three scheduling approaches.

多工作流通常部署在云平台上,以实现高效的计算能力。任务配置要求的多样性、云服务器的异构性和动态电价为经济地调度多工作流带来了巨大挑战。在本文中,我们提出了一种启发式电费感知多工作流调度算法(HEMS)来搜索最优调度方案,该方案为每个工作流中的每个任务确定最优调度方案,指定服务器在特定时间内利用确定的资源执行任务。其目标是在满足所有工作流的截止日期限制的同时,最大限度地降低所有服务器的总电费。HEMS 算法由五个部分组成:工作流调度序列生成、每个工作流的任务调度序列初始化、每个任务的最优调度方案确定、初始任务调度序列优化和最优调度计划优化。实验结果表明,与现有的三种调度方法相比,对于不同的多工作流,HEMS 可以在稍长的 CPU 时间内,以较低的总电费(平均节省 54.5-69.1%)实现最优调度方案。
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引用次数: 0
A multi-objective crow search algorithm for optimizing makespan and costs in scientific cloud workflows (CSAMOMC) 用于优化科学云工作流中的时间跨度和成本的多目标乌鸦搜索算法(CSAMOMC)
IF 3.7 3区 计算机科学 Q2 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-02-24 DOI: 10.1007/s00607-024-01263-4
Reza Akraminejad, Navid Khaledian, Amin Nazari, Marcus Voelp

Nowadays, with the rapid expansion of cloud computing technology in processing Internet of Things (IoT) workloads, the demand for data centers has significantly increased, leading to a surge in CO2 emissions, power consumption, and global warming. As a result, extensive research and initiatives have been undertaken to tackle this problem. Two specific approaches focus on enhancing workload scheduling, a complex problem known as NP-Hard, and integrating scheduling into scientific workflows. In this investigation, we present a multi-objective Crow Search Algorithm (CSA) for optimizing both makespan and costs in scientific cloud workflows (CSAMOMC). We conduct a comparative analysis between our approach and the well-known HEFT and TC3pop algorithms, which are commonly used for reducing makespan and optimizing costs. Our findings demonstrate that CSAMOMC is capable of achieving an average makespan reduction of 4.42% and a cost reduction of 4.77% when compared to the aforementioned algorithms.

如今,随着云计算技术在处理物联网(IoT)工作负载方面的迅速扩展,对数据中心的需求大幅增加,导致二氧化碳排放量、电力消耗和全球变暖问题激增。因此,为解决这一问题,人们开展了广泛的研究和行动。两种具体方法分别侧重于加强工作负载调度(一个被称为 NP-Hard 的复杂问题)和将调度整合到科学工作流中。在这项研究中,我们提出了一种多目标乌鸦搜索算法(CSA),用于优化科学云工作流(CSAMOMC)中的时间跨度和成本。我们将我们的方法与著名的 HEFT 算法和 TC3pop 算法进行了比较分析,这两种算法通常用于缩短时间跨度和优化成本。我们的研究结果表明,与上述算法相比,CSAMOMC 能够将平均有效期缩短 4.42%,将成本降低 4.77%。
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引用次数: 0
Enhancing sine cosine algorithm based on social learning and elite opposition-based learning 基于社会学习和精英对抗学习的正弦余弦算法的改进
IF 3.7 3区 计算机科学 Q2 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-02-24 DOI: 10.1007/s00607-024-01256-3
Lei Chen, Linyun Ma, Lvjie Li

In recent years, Sine Cosine Algorithm (SCA) is a kind of meta-heuristic optimization algorithm with simple structure, simple parameters and trigonometric function principle. It has been proved that it has good competitiveness among the existing optimization algorithms. However, the single mechanism of SCA leads to its insufficient utilization of the information of the whole population, insufficient ability to jump out of local optima and poor performance at solving complex objective function. Therefore, this paper introduces social learning strategy (SL) and elite opposition-based learning (EOBL) strategy to improve SCA, and proposes novel algorithm: enhancing Sine Cosine Algorithm based on elite opposition-based learning and social learning (ESLSCA). Social learning strategy takes full advantage of information from the entire population. The elite opposition-based learning strategy provides a possibility for the algorithm to jump out of local optima and increases the diversity of the population. To demonstrate the performance of ESLSCA, this paper uses 22 well-known benchmark test functions and CEC2019 test function set to evaluate ESLSCA. The comparisons show that the proposed ESLSCA has better performance than the standard SCA and it is very competitive among other excellent optimization algorithms.

近年来,正弦余弦算法(SCA)是一种元启发式优化算法,具有结构简单、参数简单、三角函数原理等特点。实践证明,它在现有的优化算法中具有很强的竞争力。然而,由于 SCA 机制单一,导致其对全群信息的利用率不高,跳出局部最优的能力不足,求解复杂目标函数的性能较差。因此,本文引入社会学习策略(SL)和基于精英对立学习(EOBL)策略来改进 SCA,并提出了新算法:基于基于精英对立学习和社会学习的增强正余弦算法(ESLSCA)。社会学习策略充分利用了整个群体的信息。基于精英对立的学习策略为算法跳出局部最优提供了可能,并增加了群体的多样性。为了证明 ESLSCA 的性能,本文使用了 22 个著名的基准测试函数和 CEC2019 测试函数集来评估 ESLSCA。比较结果表明,所提出的 ESLSCA 比标准 SCA 性能更好,在其他优秀优化算法中具有很强的竞争力。
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引用次数: 0
SVFLDetector: a decentralized client detection method for Byzantine problem in vertical federated learning SVFLD检测器:垂直联合学习中拜占庭问题的分散客户端检测方法
IF 3.7 3区 计算机科学 Q2 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-02-21 DOI: 10.1007/s00607-024-01262-5
Jiuyun Xu, Yinyue Jiang, Hanfei Fan, Qiqi Wang

In recent years, with the deepening of cross-industry cooperation, vertical federated learning with multiple overlapping samples and fewer overlapping features has attracted extensive attention. Vertical federated learning increases the challenge of detecting Byzantine clients due to feature heterogeneity, in contrast to horizontal federated learning. Existing methods for detecting Byzantine clients can be divided into statistical-based and detection-based types. The detection-based type breaks the limit on the number of Byzantine clients. To our knowledge, current research in vertical federated learning relies on the assumption of a reliable third-party coordinator and is based on statistical type. In this work, we propose a framework based on a detection type called SVFLDetector to detect Byzantine clients in vertical federated learning. The key ideas of SVFLDetector are: (1) we combine decentralized vertical federated learning with split learning, utilizing their respective advantages and eliminating the impact of a third-party server; (2) according to the heterogeneity of features in vertical federated learning, we use a client detection method which is achieved by grouping through feature encoding and performing cross validation within groups to identify Byzantine clients; (3) we propose a penalty function to reduce the impact of Byzantine clients on model aggregation. Numerical experiments show that our method has strong robustness against various Byzantine attacks.

近年来,随着跨行业合作的不断深入,具有多个重叠样本和较少重叠特征的垂直联合学习引起了广泛关注。与水平联合学习相比,垂直联合学习由于特征的异质性,增加了检测拜占庭客户的挑战。检测拜占庭客户机的现有方法可分为基于统计的方法和基于检测的方法。基于检测的类型打破了拜占庭客户端数量的限制。据我们所知,目前在垂直联合学习方面的研究依赖于可靠的第三方协调者的假设,并且是基于统计类型的。在这项工作中,我们提出了一个基于名为 SVFLDetector 的检测类型的框架,用于检测垂直联合学习中的拜占庭客户。SVFLDetector 的主要思想是(1)我们将去中心化的垂直联合学习与拆分学习结合起来,利用它们各自的优势,消除第三方服务器的影响;(2)根据垂直联合学习中特征的异质性,我们使用一种客户端检测方法,通过特征编码分组,并在组内进行交叉验证来识别拜占庭客户端;(3)我们提出了一种惩罚函数,以减少拜占庭客户端对模型聚合的影响。数值实验表明,我们的方法对各种拜占庭攻击具有很强的鲁棒性。
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引用次数: 0
A comparative study of LSTM-ED architectures in forecasting day-ahead solar photovoltaic energy using Weather Data 利用气象数据预测太阳能光伏发电日预报的 LSTM-ED 架构比较研究
IF 3.7 3区 计算机科学 Q2 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-02-20 DOI: 10.1007/s00607-024-01266-1
Ekin Ekinci

Solar photovoltaic (PV) energy, with its clean, local, and renewable features, is an effective complement to traditional energy sources today. However, the photovoltaic power system is highly weather-dependent and therefore has unstable and intermittent characteristics. Despite the negative impact of these features on solar sources, the increase in worldwide installed PV capacity has made solar energy prediction an important research topic. This study compares three encoder-decoder (ED) networks for day-ahead solar PV energy prediction: Long Short-Term Memory ED (LSTM-ED), Convolutional LSTM ED (Conv-LSTM-ED), and Convolutional Neural Network and LSTM ED (CNN-LSTM-ED). The models are tested using 1741-day-long datasets from 26 PV panels in Istanbul, Turkey, considering both power and energy output of the panels and meteorological features. The results show that the Conv-LSTM-ED with 50 iterations is the most successful model, achieving an average prediction score of up to 0.88 over R-square (R2). Evaluation of the iteration counts’ effect reveals that the Conv-LSTM-ED with 50 iterations also yields the lowest Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) values, confirming its success. In addition, the fitness and effectiveness of the models are evaluated, with the Conv-LSTM-ED achieving the lowest Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) values for each iteration. The findings of this work can help researchers build the best data-driven methods for forecasting PV solar energy based on PV features and meteorological features.

太阳能光伏发电(PV)具有清洁、本地和可再生的特点,是当今传统能源的有效补充。然而,光伏发电系统高度依赖天气,因此具有不稳定和间歇性的特点。尽管这些特点对太阳能产生了负面影响,但随着全球光伏发电装机容量的增加,太阳能预测已成为一个重要的研究课题。本研究比较了三种用于日前太阳能光伏发电能量预测的编码器-解码器(ED)网络:长短期记忆 ED (LSTM-ED)、卷积 LSTM ED (Conv-LSTM-ED) 以及卷积神经网络和 LSTM ED (CNN-LSTM-ED)。这些模型使用来自土耳其伊斯坦布尔 26 个光伏电池板的 1741 天数据集进行了测试,同时考虑了电池板的功率和能量输出以及气象特征。结果表明,迭代次数为 50 次的 Conv-LSTM-ED 是最成功的模型,在 R-square (R2) 上取得了高达 0.88 的平均预测分数。对迭代次数效果的评估显示,迭代 50 次的 Conv-LSTM-ED 模型的均方根误差(RMSE)和平均绝对误差(MAE)值也是最低的,这证明了它的成功。此外,还对模型的适配性和有效性进行了评估,Conv-LSTM-ED 在每次迭代中都获得了最低的 Akaike 信息准则(AIC)和贝叶斯信息准则(BIC)值。这项工作的发现有助于研究人员根据光伏特征和气象特征建立最佳的数据驱动型光伏太阳能预测方法。
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引用次数: 0
Efficient processing of all neighboring object group queries with budget range constraint in road networks 高效处理道路网络中带有预算范围限制的所有相邻对象组查询
IF 3.7 3区 计算机科学 Q2 COMPUTER SCIENCE, THEORY & METHODS Pub Date : 2024-02-16 DOI: 10.1007/s00607-024-01260-7
Yuan-Ko Huang, Chien-Pang Lee

We present a new type of location-based queries, namely the Budget Range-based All Neighboring Object Group Query (BR-ANOGQ for short), to offer spatial object information while respecting distance and budget range constraints. This query type finds utility in numerous practical scenarios, such as assisting travelers in selecting fitting destinations for their journeys. To support the BR-ANOGQ, we develop data structures for efficient representation of road networks and employ two index structures, the (R^{cC})-tree and the grid index, for managing spatial objects based on their locations and costs. We introduce two pruning criteria to filter out object sets that do not meet the specified distance d and budget range ([bgt_m, bgt_M]) constraints. We also devise a road network traversal method that selectively accesses a small fraction of objects while generating the query result. The BR-ANOGQ algorithm effectively utilizes index structures and pruning criteria for query processing. Through a series of comprehensive experiments, we demonstrate its efficiency in terms of CPU time and index node accesses, providing valuable insights for location-based queries with constraints.

我们提出了一种新型基于位置的查询,即基于预算范围的所有邻近对象组查询(简称 BR-ANOGQ),在尊重距离和预算范围限制的同时提供空间对象信息。这种查询类型在许多实际场景中都很有用,例如帮助旅行者选择合适的旅行目的地。为了支持BR-ANOGQ,我们开发了高效表示道路网络的数据结构,并采用了两种索引结构--(R^{c})树和网格索引--来根据空间对象的位置和成本管理它们。我们引入了两个剪枝标准来过滤不符合指定距离 d 和预算范围 ([bgt_m, bgt_M]) 约束的对象集。我们还设计了一种路网遍历方法,在生成查询结果时选择性地访问一小部分对象。BR-ANOGQ 算法有效地利用了索引结构和剪枝标准进行查询处理。通过一系列综合实验,我们证明了该算法在 CPU 时间和索引节点访问方面的效率,为基于位置的约束查询提供了有价值的见解。
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引用次数: 0
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