异构三维片上网络布局优化的超图划分算法

片上网络作为一种将大量嵌入式内核集成到单个晶圆片上的可行性技术,与传统片上系统相比,更能应对未来需要更大规模集成内核的挑战,从而得到了更广泛的应用。然而,目前大多数对片上网络的研究是在规则的架构上进行的,即假定所有单元片面积相同,但是这种假设过于理想化。因此,基于异构布局的三维片上网络的研究是非常有必要的,而其中网络单元的合理划分对片上网络的性能有着重要的影响。介绍了基于异构布局的三维片上网络架构,并将超大规模集成网络中的单元映射成一张超图,并且对此超图进行了多级划分。在算法框架的不同阶段,介绍了常见的算法,并且对相应算法的潜在问题进行分析,随后对这几种算法进行改进以提高片上网络的性能。最后,通过对几个常见的超大规模集成单元数据集进行实验分析,比较了不同阶段的算法对该片上网络各个性能的影响,并得出各个数据集上最优的hMetis算法框架。     

多级划分算法的后处理与评价方法

多级划分算法需要进行多次实验以得到最优值.本文根据网表顶点在多次实验中的倾向性将其分为:活跃点、固定点和亚固定点,并提出只对活跃点重新划分的后处理方法.另外,通过将固定点和亚固定点分配到相应簇中,得到一种算法评价方法.实验表明,本文的后处理方法可有效减小hMetis算法的最小割,而评价方法能够客观评价hMetis算法在不同聚类策略下的划分结果.     

赋权超图划分算法的电路划分实验比较研究

给出了赋权超图优化划分问题的形式化描述,并结合电路划分的具体应用,采用赋权超图来构造ISPD98电路测试基准的数学模型。阐述了基于迁移方法和多水平方法的赋权超图优化划分算法,并重点讨论了粗化阶段的不同结点匹配策略、迁移优化阶段的不同结点迁移优化策略。基于ISPD98测试基准给出的18 组电路,进行了迁移方法和多水平方法的对比实验,以及五种结点匹配和三种结点迁移优化不同组合策略的对比实验,实验数据对比充分验证了多水平方法的可行性和效率。     

面向超图数据的最大独立集算法

超图是普通图的泛化表示, 在许多应用领域都很常见, 包括互联网、生物信息学和社交网络等. 独立集问题是图分析领域的一个基础性研究问题, 传统的独立集算法大多都是针对普通图数据, 如何在超图数据上实现高效的最大独立集挖掘是一个亟待解决的问题. 针对这一问题, 提出一种超图独立集的定义. 首先分析超图独立集搜索的两个特性, 然后提出一种基于贪心策略的基础算法. 接着提出一种超图近似最大独立集搜索的剪枝框架即精确剪枝与近似剪枝相结合, 以精确剪枝策略缩小图的规模, 以近似剪枝策略加快搜索速度. 此外, 还提出4种高效的剪枝策略, 并对每种剪枝策略进行理论证明. 最后, 通过在10个真实超图数据集上进行实验, 结果表明剪枝算法可以高效地搜索到更接近于真实结果的超图最大独立集.     

低功耗驱动的电路网表多级划分算法

在划分阶段因得不到实际线长值而无法精确计算功耗值.通过组合使用互连线的通路级数、通路级差和基本线长,提出一种新的独立线长预测方法.使用预测线长和开关活动性的乘积度量划分阶段的动态功耗,并将这一乘积作为权重赋给每条互连线;在聚类和细化处理阶段,尽量避免权重较大的互连线被分割,以实现低功耗驱动的多级划分.实验结果表明,该算法可有效地减小电路的功耗,并且对其他技术指标影响不大.     

一种松弛的优化均衡流式图划分算法研究

在大规模图数据的分布式处理中,往往需要将图数据进行划分并放置在不同的节点上。如果数据划分得不均衡,那么部分节点可能会成为分布式系统的瓶颈。为了提高图数据划分的均衡性,并且有效地应对图数据的快速更新,提出了一种松弛的优化均衡流式图划分算法。首先,定义了一种同时包含划分内部代价和划分之间的割的代价的目标函数作为图划分的整体框架。然后,在图划分框架的基础上通过最大化和最小化两种优化函数分析了均衡图划分问题,并给出了二者之间的关系。最后,针对流式图数据,提出一种贪婪的图最优k划分算法。该划分算法以最大化优化函数为基础,通过最大化顶点放置产生的目标函数增加值进行节点划分块的选取。实验表明,提出的图划分算法与相关算法相比,不仅均衡性好,而且通信开销小,在基于该算法进行图划分时上层应用的计算性能得到了明显的提高。     

GPLP:基于标签传播的大图多级划分算法

图数据划分问题是大图处理系统的关键问题,制约着图处理系统的计算效率。目前可用的划分算法可分为随机划分和多层次划分,已有的算法难以在划分速度和划分效果两个方面同时满足要求。提出了一种新的基于标签传播的多级划分算法GPLP,该方法将图划分过程分为数据标记、图粗糙化和数据迁移三部分,在多级划分框架下采用标签传播算法,并对其进行了改进。从数据划分时间和迭代计算时间两个方面对比GPLP算法、Hash算法和Par METIS算法的性能,实验结果表明GPLP算法能够提高迭代计算速度,减少了划分时间,并且数据规模越大,其优势越明显。     

基于联合权重超图划分的SNN负载均衡方法

大规模脉冲神经网络并行模拟是探究大脑机能的重要手段。其难点在于合理地将负载映射到并行分布式平台上,提升模拟速度。为解决该问题,提出一种基于联合权重超图划分的SNN负载均衡方法,解决并行计算中进程间计算负载与通信负载的均衡问题,提高SNN模拟速度。并使用稀疏通信的方式替代集体通信,解决事件通信过程中的数据冗余问题,提升通信效率。实验结果表明,该方法使带有STDP突触20%规模的皮质层微电路模型的模拟时间,比标准循环分配算法缩短约64.5%,比普通超图分配算法缩短约57.4%,同时事件通信数据量减少了90%以上。     

基于再聚类和离散优化的k路划分算法

为了寻得集成电路更优的k路划分,提出将再聚类和离散优化应用于k路划分算法.首先利用再聚类缩小超图规模,即根据给定划分计算顶点间的评级函数值,依据取值大小进行顶点聚类;然后将超图转换为星型图,并将k路划分问题转换为无约束的离散优化问题;进而设计一个算法迭代移动增益值最大的顶点,在算法求解过程中放宽平衡约束,允许暂时处于不可行域的解,扩大问题的求解空间.在同一平台上使用ISPD98电路测试基准对所提算法、hMETIS-Kway和KaHyPar-K进行测试,并比较最小割值和运行时间.实验结果表明该算法优于hMETIS-Kway,特别是在k=2时,最小割值减少了0.173,速度提升了0.706.此外,该算法对KaHyPar-K也有相应的改进效果.     

与体系结构匹配的多级可重构任务划分方法

异构系统是高性能计算发展的主要模式,云计算是异构计算的典型实例。其优势在于异构处理器能各尽其能,但在实际应用中异构系统的性能往往不能充分发挥,因为处理器特征与应用程序特征不匹配,造成系统效率低下。因此借助重构思想,提出与体系结构结合的多级可重构任务划分方法。定义了多级可重构的概念,分析了异构匹配的原理,给出异构特征分析过程,提出了基于异构特征匹配的多级可重构任务划分方法。最后通过仿真实验说明,与体系结构匹配的划分方法适合当前的异构系统。     

Parallel multilevel algorithms for hypergraph partitioning

In this paper, we present parallel multilevel algorithms for the hypergraph partitioning problem. In particular, we describe for parallel coarsening, parallel greedy k-way refinement and parallel multi-phase refinement. Using an asymptotic theoretical performance model, we derive the isoefficiency function for our algorithms and hence show that they are technically scalable when the maximum vertex and hyperedge degrees are small. We conduct experiments on hypergraphs from six different application domains to investigate the empirical scalability of our algorithms both in terms of runtime and partition quality. Our findings confirm that the quality of partition produced by our algorithms is stable as the number of processors is increased while being competitive with those produced by a state-of-the-art serial multilevel partitioning tool. We also validate our theoretical performance model through an isoefficiency study. Finally, we evaluate the impact of introducing parallel multi-phase refinement into our parallel multilevel algorithm in terms of the trade off between improved partition quality and higher runtime cost.     

Salient object detection using content-sensitive hypergraph representation and partitioning

As an important problem in image understanding, salient object detection is essential for image classification, object recognition, as well as image retrieval. In this paper, we propose a new approach to detect salient objects from an image by using content-sensitive hypergraph representation and partitioning. Firstly, a polygonal potential Region-Of-Interest (p-ROI) is extracted through analyzing the edge distribution in an image. Secondly, the image is represented by a content-sensitive hypergraph. Instead of using fixed features and parameters for all the images, we propose a new content-sensitive method for feature selection and hypergraph construction. In this method, the most discriminant color channel which maximizes the difference between p-ROI and the background is selected for each image. Also the number of neighbors in hyperedges is adjusted automatically according to the image content. Finally, an incremental hypergraph partitioning is utilized to generate the candidate regions for the final salient object detection, in which all the candidate regions are evaluated by p-ROI and the best match one will be the selected as final salient object. Our approach has been extensively evaluated on a large benchmark image database. Experimental results show that our approach can not only achieve considerable improvement in terms of commonly adopted performance measures in salient object detection, but also provide more precise object boundaries which is desirable for further image processing and understanding.     

High-dimensional clustering: a clique-based hypergraph partitioning framework

Hypergraph partitioning has been considered as a promising method to address the challenges of high-dimensional clustering. With objects modeled as vertices and the relationship among objects captured by the hyperedges, the goal of graph partitioning is to minimize the edge cut. Therefore, the definition of hyperedges is vital to the clustering performance. While several definitions of hyperedges have been proposed, a systematic understanding of desired characteristics of hyperedges is still missing. To that end, in this paper, we first provide a unified clique perspective of the definition of hyperedges, which serves as a guide to define hyperedges. With this perspective, based on the concepts of shared (reverse) nearest neighbors, we propose two new types of clique hyperedges and analyze their properties regarding purity and size issues. Finally, we present an extensive evaluation using real-world document datasets. The experimental results show that, with shared (reverse) nearest neighbor-based hyperedges, the clustering performance can be improved significantly in terms of various external validation measures without the need for fine tuning of parameters.     

Multi-level direct K-way hypergraph partitioning with multiple constraints and fixed vertices

K$K$-way hypergraph partitioning has an ever-growing use in parallelization of scientific computing applications. We claim that hypergraph partitioning with multiple constraints and fixed vertices should be implemented using direct K$K$-way refinement, instead of the widely adopted recursive bisection paradigm. Our arguments are based on the fact that recursive-bisection-based partitioning algorithms perform considerably worse when used in the multiple constraint and fixed vertex formulations. We discuss possible reasons for this performance degradation. We describe a careful implementation of a multi-level direct K$K$-way hypergraph partitioning algorithm, which performs better than a well-known recursive-bisection-based partitioning algorithm in hypergraph partitioning with multiple constraints and fixed vertices. We also experimentally show that the proposed algorithm is effective in standard hypergraph partitioning.     

Parallel computation of continuous Petri nets based on hypergraph partitioning

Continuous Petri net can be used for performance analysis or static analysis. The analysis is based on solving the associated ordinary differential equations. This paper presents a method to parallel compute these differential equations. We first map the Petri net to a hypergraph, and then partition the hypergraph to minimize interprocessor communication while maintaining a good load balance; Based on the partition result, we divide the differential equations into several blocks; Finally, we design a parallel computing algorithm to compute these equations. Software hMETIS is used to partition the hypergraph, and software SUNDIALS is used to support the parallel computing of differential equations. Gas station problem and dining philosopher problem have been used to demonstrate the feasibility, accuracy, and scalability of our method.     

Adaptive hypergraph superpixels

Superpixel segmentation, which amounts to partitioning an image into a number of superpixels each of which is a set of pixels sharing common visual meanings, requires specific needs for different computer vision tasks. Graph based methods, as a kind of popular superpixel segmentation method, regard an image as a weighted graph whose nodes correspond to pixels of the image, and partition all pixels into superpixels according to the similarity between pixels over various feature spaces. Despite their improvement of the performance of segmentation, these methods ignore high-order relationship between them incurred from either locally neighboring pixels or structured layout of the image. Moreover, they measure the similarity of pairwise pixels using Gaussian kernel where a robust radius parameter is difficult to find for pixels which exhibit multiple features (e.g., texture, color, brightness). In this paper, we propose an adaptive hypergraph superpixel segmentation (AHS) of intensity images for solving both issues. AHS constructs a hypergraph by building the hyperedges with an adaptive neighborhood scheme, which explores an intrinsic relationship of pixels. Afterwards, AHS encodes the relationship between pairwise pixels using characteristics of current two pixels as well as their neighboring pixels defined by hyperedges. Essentially, AHS models the relationship of pairwise pixels in a high-order group fashion while graph based methods evaluate it in a one-vs-one fashion. Experiments on four datasets demonstrate that AHS achieves higher or comparable performance compared with state-of-the-art methods.     

Testing hypergraph colorability

We study the problem of testing properties of hypergraphs. The goal of property testing is to distinguish between the case whether a given object has a certain property or is “far away” from the property. We prove that the fundamental problem of $\ell$-colorability of k-uniform hypergraphs can be tested in time independent of the size of the hypergraph. We present a testing algorithm that examines only $(k\ell /\epsilon {)}^{\mathrm{O}(k)}$ entries of the adjacency matrix of the input hypergraph, where $\epsilon$ is a distance parameter independent of the size of the hypergraph. The algorithm tests only a constant number of entries in the adjacency matrix provided that $\ell$, k, and $\epsilon$ are constants. This result is a generalization of previous results about testing graph colorability.     

Online hypergraph coloring

In this paper we investigate the online hypergraph coloring problem. In this online problem the algorithm receives the vertices of the hypergraph in some order v₁,…,vn and it must color vi by only looking at the subhypergraph Hi=(Vi,Ei) where Vi={v₁,…,vi} and Ei contains the edges of the hypergraph which are subsets of Vi. We show that there exists no online hypergraph coloring algorithm with sublinear competitive ratio. Furthermore we investigate some particular classes of hypergraphs (k-uniform hypergraphs, hypergraphs with bounded matching number, projective planes), we analyse the online algorithm FF and give matching lower bounds for these classes.     

Entropic measure and hypergraph states

We investigate some properties of the entanglement of hypergraph states in purely hypergraph theoretical terms. We first introduce an approach for computing local entropic measure on qubit $t$ of a hypergraph state by using the Hamming weight of the so-called $t$ -adjacent subhypergraph. Then, we quantify and characterize the entanglement of hypergraph states in terms of local entropic measures obtained by using the above approach. Our results show that full-rank hypergraph states of more than two qubits can not be converted into any graph state under local unitary transformations.