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Proper Coloring Distance in Edge-Colored Cartesian Products of Complete Graphs and Cycles 完全图与环的边色笛卡尔积的适当着色距离
Pub Date : 2019-12-01 DOI: 10.1142/s0129626419500166
Ajay Arora, E. Cheng, Colton Magnant
An path that is edge-colored is called proper if no two consecutive edges receive the same color. A general graph that is edge-colored is called properly connected if, for every pair of vertices in the graph, there exists a properly colored path from one to the other. Given two vertices u and v in a properly connected graph G, the proper distance is the length of the shortest properly colored path from u to v. By considering a specific class of colorings that are properly connected for Cartesian products of complete and cyclic graphs, we present results on the proper distance between all pairs of vertices in the graph.
如果没有两条连续的边获得相同的颜色,则称为正确的路径。如果对于图中的每一对顶点,存在一条从一个顶点到另一个顶点的适当着色的路径,则称为正确连通的一般图。给定适当连通图G中的两个顶点u和v,固有距离是u到v的最短适当着色路径的长度。通过考虑完全图和循环图的笛卡尔积的适当连通的一类特定着色,我们给出了图中所有顶点对之间的固有距离的结果。
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引用次数: 0
The Restricted Edge-Connectivity of Kronecker Product Graphs Kronecker积图的受限边连通性
Pub Date : 2019-10-01 DOI: 10.1142/s0129626419500129
Tianlong Ma, Jinling Wang, Mingzu Zhang
The restricted edge-connectivity of a connected graph [Formula: see text], denoted by [Formula: see text], if exists, is the minimum number of edges whose deletion disconnects the graph such that each connected component has at least two vertices. The Kronecker product of graphs [Formula: see text] and [Formula: see text], denoted by [Formula: see text], is the graph with vertex set [Formula: see text], where two vertices [Formula: see text] and [Formula: see text] are adjacent in [Formula: see text] if and only if [Formula: see text] and [Formula: see text]. In this paper, it is proved that [Formula: see text] for any graph [Formula: see text] and a complete graph [Formula: see text] with [Formula: see text] vertices, where [Formula: see text] is minimum edge-degree of [Formula: see text], and a sufficient condition such that [Formula: see text] is [Formula: see text]-optimal is acquired.
连通图[公式:见文]的受限边连通性,用[公式:见文]表示,如果存在,则是图中被删除的边的最小数量,使得每个连通的组件至少有两个顶点。图[公式:见文]和图[公式:见文]的Kronecker积,用[公式:见文]表示,是具有顶点集[公式:见文]的图,当且仅当[公式:见文]和[公式:见文]两个顶点[公式:见文]和[公式:见文]在[公式:见文]中相邻。本文证明了对于任意图[公式:见文]和具有[公式:见文]顶点的完全图[公式:见文],[公式:见文]是[公式:见文]的最小边度,获得了[公式:见文]为[公式:见文]最优的充分条件。
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引用次数: 2
Applied On-Chip Machine Learning for Dynamic Resource Control in Multithreaded Processors 片上机器学习在多线程处理器动态资源控制中的应用
Pub Date : 2019-10-01 DOI: 10.1142/s0129626419500130
Shane Carroll, Wei-Ming Lin
In this paper, we propose a machine learning algorithm to control instruction fetch bandwidth in a simultaneous multithreaded CPU. In a simultaneous multithreaded CPU, multiple threads occupy pools of hardware resources in the same clock cycle. Under some conditions, one or more threads may undergo a period of inefficiency, e.g., a cache miss, thereby inefficiently using shared resources and degrading the performance of other threads. If these inefficiencies can be identified at runtime, the offending thread can be temporarily blocked from fetching new instructions into the pipeline and given time to recover from its inefficiency, and prevent the shared system resources from being wasted on a stalled thread. In this paper, we propose a machine learning approach to determine when a thread should be blocked from fetching new instructions. The model is trained offline and the parameters embedded in a CPU, which can be queried with runtime statistics to determine if a thread is running inefficiently and should be temporarily blocked from fetching. We propose two models: a simple linear model and a higher-capacity neural network. We test each model in a simulation environment and show that system performance can increase by up to 19% on average with a feasible implementation of the proposed algorithm.
在本文中,我们提出了一种机器学习算法来控制同步多线程CPU中的指令获取带宽。在并发多线程CPU中,多个线程在同一个时钟周期内占用硬件资源池。在某些情况下,一个或多个线程可能会经历一段时间的低效率,例如,缓存丢失,从而低效地使用共享资源并降低其他线程的性能。如果可以在运行时识别这些低效率,则可以暂时阻止问题线程向管道中获取新指令,并给予时间从低效率中恢复,并防止共享系统资源浪费在停滞的线程上。在本文中,我们提出了一种机器学习方法来确定何时应该阻止线程获取新指令。该模型是离线训练的,参数嵌入到CPU中,可以通过运行时统计信息查询CPU,以确定线程是否运行效率低下,是否应该暂时阻止提取。我们提出了两个模型:一个简单的线性模型和一个高容量的神经网络。我们在仿真环境中对每个模型进行了测试,结果表明,通过提出的算法的可行实现,系统性能平均可提高19%。
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引用次数: 2
Quantum Fuzzy Game Simulation 量子模糊博弈仿真
Pub Date : 2019-10-01 DOI: 10.1142/s0129626419500105
R. Alonso-Sanz, Haozhen Situ
This article studies quantum games with imprecise payoffs simulated by means of fuzzy numbers. Three two-person game-types are scrutinized via the iterated confronting of a large number of players laying in a two-dimensional lattice. In every iteration, every player interacts with his nearest neighbours and adopts the strategy of his best paid mate. Variable degree of quantum entanglement and of optimism in the fuzzy payoffs are taken into consideration in the study.
本文研究了用模糊数模拟具有不精确收益的量子博弈。通过在二维格子中大量玩家的迭代对抗,仔细检查了三种双人游戏类型。在每次迭代中,每个玩家都与他最近的邻居互动,并采用他最赚钱的伙伴的策略。研究中考虑了量子纠缠度的变化和模糊收益的乐观性。
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引用次数: 1
The Connectivity of a Bipartite Graph and Its Bipartite Complementary Graph 二部图及其二部补图的连通性
Pub Date : 2019-09-26 DOI: 10.1142/S0129626420400058
Yingzhi Tian, Huaping Ma, Liyun Wu
In 1956, Nordhaus and Gaddum gave lower and upper bounds on the sum and the product of the chromatic number of a graph and its complement, in terms of the order of the graph. Since then, any bound on the sum and/or the product of an invariant in a graph [Formula: see text] and the same invariant in the complement [Formula: see text] of [Formula: see text] is called a Nordhaus-Gaddum type inequality or relation. The Nordhaus-Gaddum type inequalities for connectivity have been studied by several authors. For a bipartite graph [Formula: see text] with bipartition ([Formula: see text]), its bipartite complementary graph [Formula: see text] is a bipartite graph with [Formula: see text] and [Formula: see text] and [Formula: see text]. In this paper, we obtain the Nordhaus-Gaddum type inequalities for connectivity of bipartite graphs and its bipartite complementary graphs. Furthermore, we prove that these inequalities are best possible.
1956年,Nordhaus和Gaddum根据图的阶,给出了图的色数与补的和与积的下界和上界。此后,图[公式:见文]中的一个不变量与[公式:见文]的补[公式:见文]中的同一个不变量的和和/或积的任何界称为诺德豪斯-加德姆型不等式或关系。关于连通性的Nordhaus-Gaddum型不等式已经被一些作者研究过。对于具有双分([公式:见文])的二部图[公式:见文],其二部互补图[公式:见文]是具有[公式:见文]、[公式:见文]和[公式:见文]的二部图。本文得到了二部图及其二部补图的连通性的Nordhaus-Gaddum型不等式。进一步,我们证明了这些不等式是最佳可能的。
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引用次数: 0
A Note of Independent Number and Domination Number of Qn, k, m-Graph 图Qn, k, m的独立数和支配数的注记
Pub Date : 2019-09-01 DOI: 10.1142/s0129626419500117
Jiafei Liu, Shuming Zhou, Zhendong Gu, Yihong Wang, Qianru Zhou
The independent number and domination number are two essential parameters to assess the resilience of the interconnection network of multiprocessor systems which is usually modeled by a graph. The independent number, denoted by [Formula: see text], of a graph [Formula: see text] is the maximum cardinality of any subset [Formula: see text] such that no two elements in [Formula: see text] are adjacent in [Formula: see text]. The domination number, denoted by [Formula: see text], of a graph [Formula: see text] is the minimum cardinality of any subset [Formula: see text] such that every vertex in [Formula: see text] is either in [Formula: see text] or adjacent to an element of [Formula: see text]. But so far, determining the independent number and domination number of a graph is still an NPC problem. Therefore, it is of utmost importance to determine the number of independent and domination number of some special networks with potential applications in multiprocessor system. In this paper, we firstly resolve the exact values of independent number and upper and lower bound of domination number of the [Formula: see text]-graph, a common generalization of various popular interconnection networks. Besides, as by-products, we derive the independent number and domination number of [Formula: see text]-star graph [Formula: see text], [Formula: see text]-arrangement graph [Formula: see text], as well as three special graphs.
独立数和支配数是评价多处理机互连网络弹性的两个重要参数,多处理机互连网络弹性通常用图来建模。图[公式:见文]的独立数(用[公式:见文]表示)是任意子集[公式:见文]的最大基数,使得[公式:见文]中的两个元素在[公式:见文]中不相邻。图[公式:见文]的支配数,用[公式:见文]表示,是任意子集[公式:见文]的最小基数,使得[公式:见文]中的每个顶点要么在[公式:见文]中,要么毗邻[公式:见文]的一个元素。但到目前为止,确定图的独立数和支配数仍然是一个NPC问题。因此,确定在多处理机系统中具有潜在应用价值的特殊网络的独立网络数和控制网络数就显得尤为重要。本文首先求解了各种流行互联网络的共同概括——图的独立数和支配数的上下界的精确值。此外,作为副产物,我们导出了[公式:文]-星图[公式:文],[公式:文]-排列图[公式:文]的独立数和支配数,以及三个特殊图。
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引用次数: 0
Parallel Architecture of Reconfigurable Hardware for Massive Output Active Noise Control 面向大输出主动噪声控制的可重构硬件并行结构
Pub Date : 2019-09-01 DOI: 10.1142/s0129626419500142
Diego Mendez, David Arevalo, Diego Patino, E. Gerlein, Ricardo Quintana
Filtered-x Least Mean Squares (FxLMS) is an algorithm commonly used for Active Noise Control (ANC) systems in order to cancel undesired acoustic waves from a sound source. There is a small number of hardware designs reported in the literature, that in turn only use one reference signal, one error signal and one output control signal. In this paper, it is proposed a 3-dimensional hardware-based version of the widely used FxLMS algorithm, using one reference microphone, 18 error microphones, one output and a FIR filter of 400[Formula: see text] order. The FxLMS algorithm was implemented in a Xilinx Artix 7 FPGA running at 25 MHz, which allowed to update the filter coefficients in 32.44[Formula: see text] s. The main idea behind this work is to propose a pipelined parallelized architecture to achieve processing times faster than real time for the filter coefficients update. The main contribution of this work is not the ANC technique itself, but rather the proposed hardware implementation that utilizes integer arithmetic, which provided an acceptable error when benchmarked with a software implementation. This parallel system allows a scalable implementation as an advantage of using FPGA without compromising the computational cost and, consequently, the latency.
滤波最小均方(FxLMS)是一种常用的算法,用于主动噪声控制(ANC)系统,以消除来自声源的不需要的声波。文献中有少量的硬件设计,依次只使用一个参考信号、一个误差信号和一个输出控制信号。本文提出了一种被广泛应用的FxLMS算法的三维硬件版本,使用1个参考麦克风、18个误差麦克风、1个输出和400阶FIR滤波器。FxLMS算法在Xilinx Artix 7 FPGA上实现,运行频率为25 MHz,允许在32.44中更新滤波器系数[公式:见文本]s。这项工作背后的主要思想是提出一种流水线并行化架构,以实现滤波器系数更新的处理时间比实时更快。这项工作的主要贡献不是ANC技术本身,而是利用整数算法的拟议硬件实现,当与软件实现进行基准测试时,它提供了一个可接受的错误。这种并行系统允许可扩展的实现,作为使用FPGA的优势,而不会影响计算成本,因此,延迟。
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引用次数: 1
Elastic Parallel Systems for High Performance Cloud Computing: State-of-the-Art and Future Directions 用于高性能云计算的弹性并行系统:最新技术和未来方向
Pub Date : 2019-08-01 DOI: 10.1142/S0129626419500063
Stefan Kehrer, W. Blochinger
With on-demand access to compute resources, pay-per-use, and elasticity, the cloud evolved into an attractive execution environment for High Performance Computing (HPC). Whereas elasticity, which is often referred to as the most beneficial cloud-specific property, has been heavily used in the context of interactive (multi-tier) applications, elasticity-related research in the HPC domain is still in its infancy. Existing parallel computing theory as well as traditional metrics to analytically evaluate parallel systems do not comprehensively consider elasticity, i.e., the ability to control the number of processing units at runtime. To address these issues, we introduce a conceptual framework to understand elasticity in the context of parallel systems, define the term elastic parallel system, and discuss novel metrics for both elasticity control at runtime as well as the ex-post performance evaluation of elastic parallel systems. Based on the conceptual framework, we provide an in-depth analysis of existing research in the field to describe the state-of-the-art and compile our findings into a research agenda for future research on elastic parallel systems.
随着对计算资源的按需访问、按使用付费和弹性的增加,云逐渐成为高性能计算(HPC)的有吸引力的执行环境。弹性通常被认为是最有益的云特有属性,在交互式(多层)应用程序的环境中被大量使用,而在高性能计算领域,与弹性相关的研究仍处于起步阶段。现有的并行计算理论和传统的分析评估并行系统的指标没有全面考虑弹性,即在运行时控制处理单元数量的能力。为了解决这些问题,我们引入了一个概念框架来理解并行系统背景下的弹性,定义了弹性并行系统,并讨论了运行时弹性控制和弹性并行系统事后性能评估的新度量。基于概念框架,我们对该领域的现有研究进行了深入分析,以描述最新的研究成果,并将我们的发现汇编成弹性并行系统未来研究的研究议程。
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引用次数: 6
Scalable Sender-Based Message Logging Protocol with Little Communication Overhead for Distributed Systems 分布式系统中通信开销小的可扩展的基于发送者的消息日志记录协议
Pub Date : 2019-08-01 DOI: 10.1142/S0129626419500051
Jinho Ahn
The inherent shortcoming of the conventional Sender-Based Message Logging (SBML) protocols is to require additional control message interactions per application message to satisfy the always-no-orphans condition in case of sequential failures. In this paper, a scalable SBML protocol is introduced to lower the communication overhead by handling a sequence of messages consecutively received by each process before sending as a party. The protocol enables the process to delay the update of their receive sequence numbers to their senders until there comes out the first message it is willing to send, and then perform the collective filling out task with each sender requiring only one control message exchange. Experimental results show that our protocol outperforms the previous one in terms of the number of control messages generated.
传统的基于发送者的消息日志(SBML)协议的固有缺点是,每个应用程序消息需要额外的控制消息交互,以满足在发生顺序故障时始终没有遗漏的条件。在本文中,引入了一个可扩展的SBML协议,通过在作为一方发送之前处理每个进程连续接收的消息序列来降低通信开销。该协议允许进程延迟向发送方更新接收序列号,直到出现它愿意发送的第一条消息,然后执行集体填写任务,每个发送方只需要一次控制消息交换。实验结果表明,我们的协议在生成控制消息的数量方面优于先前的协议。
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引用次数: 3
Leader Election Requires Logarithmic Time in Population Protocols 群体协议中领袖选举需要对数时间
Pub Date : 2019-06-25 DOI: 10.1142/s012962642050005x
Y. Sudo, T. Masuzawa
This paper shows that every leader election protocol requires logarithmic stabilization time both in expectation and with high probability in the population protocol model. This lower bound holds even if each agent has knowledge of the exact size of a population and is allowed to use an arbitrarily large number of agent states. This lower bound concludes that the protocol given in [Sudo et al., SSS 2019] is time-optimal in expectation.
本文证明了在群体协议模型中,每一个领导人选举协议都需要对数的期望稳定时间和高概率稳定时间。即使每个代理都知道种群的确切规模,并且允许使用任意数量的代理状态,这个下界仍然成立。这个下界的结论是,[Sudo等人,SSS 2019]中给出的协议在期望上是时间最优的。
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引用次数: 13
期刊
Parallel Process. Lett.
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