片上P/G网求解算法及其GPU上的并行化

为了得到片上电源线/地线网络(P/G网)快速而准确的求解算法,根据结构化供电网的局部性效应,重新分析了连续过松弛迭代法(SOR)和变向隐含迭代法(ADI)在P/G网中的求解效率及并行性,提出了利于GPU加速的并行算法:G_RBSOR和G_ADI.它们均采用规则的数据结构,以利于GPU并行读写数据,并采用合并归约来并行计算迭代结束标志位.为了避免GPU计算的数据冲突,G_RBSOR算法采用棋盘格方式对电路节点进行红黑分类,并对红黑节点进行交错松弛.实验结果表明,在不损失精度的前提下,与各自对应的CPU串行算法相比,G_RBSOR和G_ADI算法均取得了超过50倍的加速效果;与高效的P/G分析串行求解算法ICCG相比,也取得了超过5倍的加速效果.     

电源线/地线网络开路电阻单故障分析方法

随着集成电路工艺进入纳米时代,供电电压波动严重影响电路性能.制造中通孔对位不准,及运行中铜导线电迁移现象.都会在电源线/地线网络(P/G网)中产生大量潜在的开路故障,并使供电电压发生明显波动.为了在测试中对大量的开路故障进行快速测试.迫切需要提高故障分析的算法效率.为此,首次提出了单故障连续过松弛算法(SD-SOR),对发生单开路电阻故障的P/G网节点电压分布进行快速分析.基于无故障P.G网节点电压分布,SD-SORR对开路电阻周围受故障影响比较大的少数节点进行松弛计算.与传统的全局SOR方法相比,SD-SOR具有如下3个优点:1)局部松弛.由于电路中只有一个电阻口发生开路故障.SD-SOR不是采用全局电路节点的顺序松弛方法,而是采用从故障q所连的节点不断向周围节点进行松弛的波状松弛方法,当某些节点的IR电压降变化小于一个极小的设定值时.这些节点就不再向外进行松弛计算.2)高效.与传统的全局SOR方法相比.SD-SOR不仅参与松弛的节点非常少.而且松弛次数也有明显减少.3)高精度.与传统的全局SOR方法相比,由于距离故障比较远,电路中绝大多数节点电压变化非常小,所以SD-SOR只需对距离故障比较近的节点进行松弛计算,就能够保持较高的分析精度.大量的实验数据表明:与预条件全局SOR求解方法相比,SD-SOR在保持较高精度(误差小于0.95%)的前提下,速度可以提高57倍.     

用于快速P/G网分析的Cholesky分解法图模型

通过对Cholesky分解法求解线性方程组的分析，建立Cholesky分解法三角化对称正定阵的图模型，并基于该模型及Mesh结构P／G网络的自身特点，提出一个P／G网快速分析算法．实验证明，该算法能大大降低Mesh结构P／G网络的分析运算时间和内存占用．     

随机行走算法研究及其在电源/地线网络瞬态优化中的应用

实验分析了电源/地线(P/G)网络的随机行走算法,与传统的预优共轭梯度法比较发现,当随机行走求解较少节点时性能较好,但在大规模P/G网络瞬态分析中相对较慢.通过修改随机行走过程进行伴随网络的瞬态分析,提出一种快速计算灵敏度的算法.实验结果表明,该算法计算时间较短,与精确结果误差较小.     

ECO布局中的电源线/地线网络局部SOR分析方法

供电电压直接决定芯片性能,在IC设计的各个阶段考虑供电电压约束具有重要的意义.受制于电源线/地线(P/G)网络分析的高复杂性,尽管供电电压已成为布图规划设计中的一个设计约束,但目前在布局设计中还未考虑供电电压约束.有别于ICCG,SOR等经典的全局分析算法,提出了一种局部的连续过松弛方法(SORPECO),并在ECO布局过程中对P/G网电压约束进行高效的分析.基于前一个布局的P/G网电压分布,针对ECO试探布局中某些轻微设计变动,SORPECO只需对这些设计变动的局部变化周边区域进行松弛,以更新P/G网电压分布.受益于P/G网络分析的局部性,SORPECO拥有局部、高效和高精度等优点.实验结果表明,与通常用于布图规划的传统高效的ICCG算法相比,SORPECO不仅精度损耗几乎可以忽略(最大误差0.062%),而且可以加速2个数量级.     

利于GPU计算具有线性并行度的P/G网SOR求解算法

近年来电子设计自动化(EDA)研究人员尝试利用图形处理器(graphic processing unit,GPU)提供的高性能计算能力对IC参数分析进行加速研究.为了利用GPU进行电源线/地线网络(power/ground network,P/G网)快速分析,设计了一种基于经典的连续过松弛(successive over-relaxation,SOR)算法的高效P/G网分析并行算法.基于GPU并行计算加速原理,此算法进行了如下改进:1)采用红-黑次序的松弛策略.将所有的节点分为红黑两类,红色节点的所有邻点只有黑色节点、黑色节点的所有邻点只有红色节点,红色节点与黑色节点交替松弛,保证了GPU并行计算中的数据一致性.对于具有N个节点的P/G网而言,一次红色节点或黑色节点松弛可以同时对N/2个节点进行松弛操作,即理论上可以同时启动N/2个并行线程.2)优化数据结构.实现了对数据空间的合并访问,以保证对GPU全局存储空间的最优访问.3)在共享存储器内通过并行归约对松弛标记进行快速统计,同时利用zero-copy技术进行松弛标记的快速拷贝,以快速决定是否继续松弛.大量的实验结果表明:与单线程的CPU程序相比,此算法的加速倍数随GPU所提供物理线程的数目增加而线性增加,可以获得最大242倍的加速效果,是目前EDA研究领域中加速效果最好的GPU算法.     

基于几何多网格的RLC电源网络的瞬态模拟

提出了一种高效的、针对VLSI中Mesh拓扑结构的RLC电源线／地线网络的时域分析算法，该算法首次利用一种基于启发式原则的电路模型的简化方法来缩小电路网络的规模，扩展了原有的几何多网格方法来模拟求解以RLC元件建模的电源线网络．实验数据表明，对于一些规模较大的电路实例，在一个较小的误差损失下，该算法能大幅缩小电路的求解规模，求解速度比SPICE快两个数量级以上，比原有的几何多网格方法也有大幅的提高．如在Sun工作站上，当误差控制在1．5％时，模拟求解一个百万节点的电路网络仅仅需要半个小时．     

局部松弛电路理论及其在电热分析中的应用

在复杂度日益增高的高性能集成电路设计中,高效的性能分析是一项重要的设计内容,其中由电源线/地线网络(P/G)分析与芯片热分析构成的电热分析则是目前研究的热点问题.针对电热分析方程所具有的大规模稀疏(电导或热导)系数矩阵,根据该系数矩阵所具有的对称正定严格对角占优等特性,本文从理论上证明了电热分析具有局部性,在相同的截断误差限松弛结束条件下,局部松弛和全局松弛具有相同的松弛精度.基于局部松弛理论,本文提出了一个高效实用的局部过松弛(SOR)算法(LSOR2),并在文章最后将其用于如下的3个具体的电热分析问题研究:(1)P/G网中的过压降点电压变化统计分析;(2)3D热分析中的过热点温度变化统计分析;(3)单开路故障下的P/G网快速分析.实验数据表明:与全局SOR算法相比,在保证精度的前提下,LSOR2算法可以将电热分析的求解速度提高1-2个数量级.     

SOC设计中的浮动压焊块电源/地线网络设计和优化

随着VLSI工艺技术的发展和芯片规模的不断增加，尤其是在SOC设计中，原有的那种供电压焊块只能位于芯片边缘的确定益的模式已经不能够满足整个电路性能的需要。在很多情况下，依靠在电源线的拓扑结构确定后的线宽优化，还是无法保证在有限的布线资源下为电路提供可靠的高性能的供电需求。由此，出现了在芯片边缘上浮动放置压焊块及在芯片的顶部放置供电压焊块阵列的方法。文中提出了一种用于SOC设计中新的基于树型结构的浮动压焊块的电源／地线网络优化算法，经过MCNC电路实例测试后得到明显的优化结果。     

无重叠条件严格模式匹配的高效求解算法

无重叠条件序列模式挖掘是一种间隙约束序列模式挖掘方法，与同类挖掘方法相比，该方法更容易发现有价值的频繁模式，其核心问题是计算给定模式在序列中的支持度或出现数，进而判定该模式的频繁性.而计算模式支持度问题实质是无重叠条件模式匹配.当前研究采用迭代搜索无重叠出现，然后剪枝无用结点的方式计算模式的支持度，其计算时间复杂度为O （m×m×n×W），其中，m，n和W分别为模式长度、序列长度及最大间隙.为了进一步提高无重叠条件模式匹配计算速度，从而有效地降低无重叠条件序列模式挖掘时间，提出了一种高效的算法，该算法将模式匹配问题转换为一棵网树，然后从网树的最小树根结点出发，采用回溯策略迭代搜索最左孩子方式计算无重叠最小出现，在网树上剪枝该出现后，无需进一步查找并剪枝无效结点即可实现问题的求解.理论证明了该算法的完备性，并将该算法的时间复杂度降低为O （m×n×W）.在此基础上，继续指明该问题还存在另外3种相似的求解策略，分别是从最左叶子出发迭代查找最左双亲方式、从最右树根出发迭代查找最右孩子方式和从最右叶子出发迭代查找最右双亲方式.实验结果验证了该算法的性能，特别是在序列模式挖掘中，应用该方法的挖掘算法可以降低挖掘时间.     

Time-domain analysis methodology for large-scale RLC circuits and its applications

With soaring work frequency and decreasing feature sizes, VLSI circuits with RLC parasitic components are more like analog circuits and should be carefully analyzed in physical design. However, the number of extracted RLC components is typically too large to be analyzed efficiently by using present analog circuit simulators like SPICE. In order to speedup the simulations without error penalty, this paper proposes a novel methodology to compress the time-descritized circuits resulted from numerical integration approximation at every time step. The main contribution of the methodology is the efficient structure-level compression of DC circuits containing many current sources, which is an important complement to present circuit analysis theory. The methodology consists of the following parts: 1) An approach is proposed to delete all intermediate nodes of RL branches. 2) An efficient approach is proposed to compress and back-solve parallel and serial branches so that it is error-free and of linear complexity to analyze circuits of tree topology. 3) The Y toπtransformation method is used to error-free reduce and back-solve the intermediate nodes of ladder circuits with the linear complexity. Thus, the whole simulation method is very accurate and of linear complexity to analyze circuits of chain topology. Based on the methodology, we propose several novel algorithms for efficiently solving RLC-model transient power/ground (P/G) networks. Among them, EQU-ADI algorithm of linear-complexity is proposed to solve RLC P/G networks with mesh-tree or mesh-chain topologies. Experimental results show that the proposed method is at least two orders of magnitude faster than SPICE while it can scale linearly in both time- and memory-complexity to solve very large P/G networks.     

Localized relaxation theory of circuits and its applications in electro-thermal analyses

In the high-performance IC design with increasing design complexity,it is a very important design content to efficiently analyze IC parameters.Thus,the electro-thermal (ET) analyses including power/ground (P/G) analysis and thermal analysis are hot topics in today’s IC research.Since ET analysis equation has a sparse,positive definite and strictly diagonally dominant coefficient-matrix,we prove that the ET analysis has the advantage of locality.Owing to this advantage,localized relaxation method is formally proposed,which has the same accuracy as the global relaxation done with the constraint of the same truncation error limitation.Based on the localized relaxation theory,an efficient and practical localized successive over-relaxation algorithm (LSOR2) is introduced and applied to solve the following three ET analysis problems.(1) Single-node statistical voltage analysis for over-IR-drop nodes in P/G networks;(2) single-node statistical temperature analysis for hot spots in 3D thermal analysis;(3) fast single open-defect analysis for P/G networks.A large amount of experimental data demonstrates that compared with the global successive over-relaxation (SOR) algorithm,LSOR2 can speed up 1-2 orders of magnitudes with the same accuracy in ET analyses.     

Exploiting multi-core nodes in peer-to-peer grids

While the majority of CPUs now sold contain multiple computing cores, current grid computing systems either ignore the multiplicity of cores, or treat them as distinct, independent machines. The latter approach ignores the resource contention present between cores in a single CPU, while the former approach fails to take advantage of significant computing power. We provide a decentralized resource management framework for exploiting multi-core nodes to run multi-threaded applications in peer-to-peer grids. We present two new load-balancing schemes that explicitly account for the resource sharing and contention of multiple cores, and propose a parameterized performance prediction model that can represent a continuum of resource sharing among cores of a CPU. We use extensive simulation to confirm that our two algorithms match jobs with computing nodes efficiently, and balance load during the lifetime of the computing jobs.     

Distributed multi-join query processing in data grids

Query processing in data grids is a difficult issue due to the heterogeneous, unpredictable and volatile behaviors of the grid resources. Applying join operations on remote relations in data grids is a unique and interesting problem. However, to the best of our knowledge, little is done to date on multi-join query processing in data grids. An approach for processing multi-join queries is proposed in this paper. Firstly, a relation-reduction algorithm for reducing the sizes of operand relations is presented in order to minimize data transmission cost among grid nodes. Then, a method for scheduling computer nodes in data grids is devised to parallel process multi-join queries. Thirdly, an innovative method is developed to efficiently execute join operations in a pipeline fashion. Finally, a complete algorithm for processing multi-join queries is given. Analytical and experimental results show the effectiveness and efficiency of the proposed approach.     

Network representation learning based on community-aware and adaptive random walk for overlapping community detection

The Network representation learning methods based on random walk aim to learn a low-dimensional embedding vector for each node in a network by randomly traversing the network to capture the features of nodes and edges, which is beneficial to many downstream machine learning tasks such as community detection. Most of the existing random-walk-based network representation learning algorithms emphasize the neighborhood of nodes but ignore the communities they may form and apply the same random walk strategy to all nodes without distinguishing the characteristics of different nodes. In addition, it is time-consuming to determine the most suitable random walk parameters for a given network. In this paper, we propose a novel overlapping community detection algorithm based on network representation learning which integrates community information into embedding vectors to improve the cohesion degree of similar nodes in the embedding space. First, a node-centrality-based walk strategy is designed to determine the parameters of random walk automatically to avoid the time-consuming manual selection. Second, two community-aware random walk strategies for high and low degree nodes are developed to capture the characteristics of the community centers and boundaries. The experimental results on the synthesized and real-world datasets demonstrate the effectiveness and efficiency of our algorithm on overlapping community detection compared with the state-of-the-art algorithms

     

Biased sampling from facebook multilayer activity network using learning automata

Although much research has been devoted to unbiased sampling of various networks, bias is not always disadvantageous, but sometimes useful. Especially for many real-world applications such as detecting influential nodes, spam users, and the most trustful people, it is preferred to sample users with special properties. Since sampling from friendship network alone cannot collect these important nodes appropriately, one may use interactions occurred among users. This paper deals with biased sampling of multilayer activity network. The proposed method initially learns the transition probabilities according to the considered application using learning automata. Then we sample the graph by running an application-based random walk following the learnt probabilities, in order to be guided to suitable nodes and collect their information. At last, the performance of the proposed method in terms of different applications such as fame, spam, and trust is evaluated and compared with those of common sampling algorithms. According to the experiments done, biased sampling method based on learning automata outperforms all other sampling approaches including simple random walk, Metropolis-Hastings random walk, BFS, forest fire, degree, and uniform sampling in terms of all the evaluation measures. To the best of our knowledge, our method is the first and only biased sampling method which can be used in a multilayer activity network.     

Graffiti: graph-based classification in heterogeneous networks

We address the problem of multi-label classification in heterogeneous graphs, where nodes belong to different types and different types have different sets of classification labels. We present a novel approach that aims to classify nodes based on their neighborhoods. We model the mutual influence of nodes as a random walk in which the random surfer aims at distributing class labels to nodes while walking through the graph. When viewing class labels as “colors”, the random surfer is essentially spraying different node types with different color palettes; hence the name Graffiti of our method. In contrast to previous work on topic-based random surfer models, our approach captures and exploits the mutual influence of nodes of the same type based on their connections to nodes of other types. We show important properties of our algorithm such as convergence and scalability. We also confirm the practical viability of Graffiti by an experimental study on subsets of the popular social networks Flickr and LibraryThing. We demonstrate the superiority of our approach by comparing it to three other state-of-the-art techniques for graph-based classification.