面向分布式图计算的平衡图划分算法

关注分布式图计算和迭代计算处理方法选择,对计算机技术应用和改善计算机性能等方面具有现实意义。传统算法计算分布式图时,切割率最小化与负载均衡性方面无法实现协调控制,且极易出现NP组合优化等系列问题。因此,以平衡图划分算法为手段,解决分布式图计算问题,重点研究平衡系数、切割边规模。扰动次数一定的条件下,引入Metis,结合平衡图划分算法,进行试验对比分析。通过对比可以发现,该算法下的分布式图割边率计算准确性高于Metis,可以满足分布式图的实际计算需求,这说明平衡图划分算法具有实践应用价值。     

利用子空间划分的局部离群数据挖掘算法

目前大多数局部离群数据挖掘算法需人为事先设置参数或阈值,且难以应用到高维数据集.给出一种新的局部离群数据挖掘算法PSO-SPLOF,该算法首先将数据集划分为互不相交的子空间,利用偏斜度判断子空间划分的优劣,并采用微粒群算法搜索最优划分子空间集;其次针对每个最优划分子空间,计算其数据对象的局部离群因子SPLOF值,并用SPLOF值来度量数据对象的局部偏离程度.最后采用离散化的天体光谱数据作为数据集,实验验证了PSO-SPLOF算法具有受人为因素影响小、伸缩性强和运算效率高等优点.     

GPP问题的骨架分析与启发式算法设计

图的划分问题(GPP)是具有广泛应用背景的典型NP-难解问题,高效启发式算法一直是该领域的研究热点.作为设计启发式算法的有力工具,GPP的骨架分析存在理论分析结果匮乏、骨架规模过小等缺陷.文中采用构造偏移GPP实例的技巧,不仅在理论卜证明了获取GPP的骨架是NP-难解的,并且利用一般GPP实例与偏移实例的关系,实现了骨架规模的提高.在此基础上,文中对于目前求解GPP问题最好的算法之一的IBS进行了改进,提出了基于偏移实例的IBS算法(BI-IBS).算法BI-IBS首先构造偏移GPP实例,然后再利用局部最优解交集对它进行归约,最后再求解归约后的规模更小的新实例.实验结果表明,BI-IBS比现有算法在解的质量上有了较显著的提高.文中的工作较完善地解决了GPP的骨架研究存在的问题,所采用的构造偏移实例的技巧对于其它NP-难解问题的骨架理论分析及启发式算法设计亦具有较高的参考价值.     

Beyond Good Partition Shapes: An Analysis of Diffusive Graph Partitioning

In this paper we study the prevalent problem of graph partitioning by analyzing the diffusion-based partitioning heuristic Bubble-FOS/C, a key component of a practical successful graph partitioner?(Meyerhenke et al. in J. Parallel Distrib. Comput. 69(9):750?C761, 2009). We begin by studying the disturbed diffusion scheme FOS/C, which computes the similarity measure used in Bubble-FOS/C and is therefore the most crucial component. By relating FOS/C to random walks, we obtain precise characterizations of the behavior of FOS/C on tori and hypercubes. Besides leading to new knowledge on FOS/C (and therefore also on Bubble-FOS/C), these characterizations have been recently used for the analysis of load balancing algorithms?(Berenbrink et al. in Proceedings of the 22nd Annual Symposium on Discrete Algorithms, pp. 429?C439, 2011). We then regard Bubble-FOS/C, which has been shown in previous experiments to produce solutions with good partition shapes and other favorable properties. In this paper we prove that it computes a relaxed solution to an edge cut minimizing binary quadratic program (BQP). This result provides the first substantial theoretical insight why Bubble-FOS/C yields good experimental results in terms of graph partitioning metrics. Moreover, we show that in bisections computed by Bubble-FOS/C, at least one of the two parts is connected. Using the aforementioned relation between FOS/C and random walks, we prove that in vertex-transitive graphs both parts must be connected components.     

面向异质图的在线图划分算法

图划分算法是分布式图计算系统里的重要组成部分, 它将一个图划分为若干子图以便在分布式系统中运行, 并将子图上的点和边数据及子图上的计算任务分配到各分区. 异质图是现实世界中广泛存在的一种图, 它是指具有多种节点类型或边类型的图, 在针对异质图的计算过程中, 现有的图划分算法对于异质图的处理没有考虑到以下问题: 在图计算过程中, 不同类型的节点和边携带的数据量可能不同; 不同的节点和边类型, 可能会采用不同的处理算法, 其计算时间也会不同. 针对现有图划分方法的不足, 本文提出一种面向异质图的在线图划分算法OGP-HG算法, 并对现有的GraphX图计算引擎进行改进, 将OGP-HG算法在改进后的图计算引擎中实现. 本文提出的OGP-HG算法通过计算节点划分到不同分区上的负载均衡得分和边划分到不同分区上的数据均衡得分, 得到使异质图负载和内存占用均衡的划分结果. 实验表明, 与传统图划分算法相比, 该算法提高异质图计算效率1.05–1.4倍.     

一种改进的并行计算图划分模型

图划分成功地应用在许多领域,但应用于并行计算时,使用边割度量通信量,其主要缺点是不能准确代表通信量,而且图划分模型没有考虑通信延迟和通信额外开销的分布对并行性能的影响.提出了改进的图划分模型,该模型将影响并行性能的多个要素(通信延迟、最大的局部通信额外开销和整体通信额外开销)整合到一个统一的代价函数,不仅克服了图划分模型中边割度量的一些缺点,而且可以通过调整加权参数,处理不同的优化目标和强调不同因素对并行性能的影响.     

Bipartite-Oriented Distributed Graph Partitioning for Big Learning

Many machine learning and data mining (MLDM) problems like recommendation, topic modeling, and medical diagnosis can be modeled as computing on bipartite graphs. However, most distributed graph-paralle...     

用神经网络求解划分问题

划分问题是一类常见的ＮＰ完备的优化问题,本文利用推广的Ｈｏｐｆｉｅｌｄ神经网络模型解决了划分问题,并取得了较好的效果,为这个总理２的解决提供了一条新的途径。同时也为解决其它优化总理２提供了有益的启示。     

Global Minimization for Continuous Multiphase Partitioning Problems Using a Dual Approach

This paper is devoted to the optimization problem of continuous multi-partitioning, or multi-labeling, which is based on a convex relaxation of the continuous Potts model. In contrast to previous efforts, which are tackling the optimal labeling problem in a direct manner, we first propose a novel dual model and then build up a corresponding duality-based approach. By analyzing the dual formulation, sufficient conditions are derived which show that the relaxation is often exact, i.e. there exists optimal solutions that are also globally optimal to the original nonconvex Potts model. In order to deal with the nonsmooth dual problem, we develop a smoothing method based on the log-sum exponential function and indicate that such a smoothing approach leads to a novel smoothed primal-dual model and suggests labelings with maximum entropy. Such a smoothing method for the dual model also yields a new thresholding scheme to obtain approximate solutions. An expectation maximization like algorithm is proposed based on the smoothed formulation which is shown to be superior in efficiency compared to earlier approaches from continuous optimization. Numerical experiments also show that our method outperforms several competitive approaches in various aspects, such as lower energies and better visual quality.     

Using Differential Evolution for a Subclass of Graph Theory Problems

Conventional differential evolution algorithms explore continuous spaces. In contrast, NP-complete graph problems are combinatorial and thus have discrete solution spaces, many with solutions encoded as binary strings. This letter describes a simple method showing how a conventional differential evolution algorithm can be used to solve these types of graph theory problems. The method is deterministic and can handle graphs of arbitrary size.     

Parallel Dynamic Graph Partitioning for Adaptive Unstructured Meshes

A parallel method for the dynamic partitioning of unstructured meshes is described. The method introduces a new iterative optimization technique known as relative gain optimization which both balances the workload and attempts to minimize the interprocessor communications overhead. Experiments on a series of adaptively refined meshes indicate that the algorithm provides partitions of an equivalent or higher quality to static partitioners (which do not reuse the existing partition) and much more rapidly. Perhaps more importantly, the algorithm results in only a small fraction of the amount of data migration compared to the static partitioners.     

一种基于空间规则度的谱图划分提取舰船编队方法

舰船编队是海上舰船巡航和作战中的重要群目标。针对编队组成和队形变化的复杂情况,本文总结了编队存在的空间规则性,由此制定模糊推理规则得到定量的空间规则度,最后用谱图划分方法提取具有较高空间规则度的编队目标。仿真和实测的数据表明,该方法可以在有干扰和编队空间关系适当变化的情况下提取出具有编队形式的群目标。     

Achieving Optimal Inter-Node Communication in Graph Partitioning Using Random Selection and Breadth-First Search

Processing large graph datasets represents an increasingly important area in computing research and applications. The size of many graph datasets has increased well beyond the processing capacity of a single computing node, thereby necessitating distributed approaches. As these datasets are processed over a distributed system of nodes, this leads to an inter-node communication cost problem that negatively affects system performance. Previously proposed algorithms implemented breadth-first search (BFS) for graph searching and focused on the execution, parallel performance and not the communication. In this paper a new methodology is proposed that combines BFS with random selection in order to partition large graph datasets and effectively minimize inter-node communication. The new method is discussed and applied to the single-source shortest path and PageRank algorithms using three graphs that are representative of real-world scenarios. Experimental results show that graph inter-node communication for canonical graphs representative of real-world data is improved up to 42 % in case of Powerlaw graph, up to 27 % in case of Random near K-regular graph (with low degree), and up to 7 % in case of Random near K-regular graph (with high degree).     

动态图划分算法研究综述

图划分是大规模分布式图处理的首要工作,对图应用的存储、查询、处理和挖掘起基础支撑作用.随着图数据规模的不断扩大,真实世界中的图表现出动态性.如何对动态图进行划分,已成为目前图划分研究的热点问题.从不同动态图划分算法的关注点和特点出发,系统性地介绍当前可用于解决动态图划分问题的各类算法,包括流式图划分算法、增量式图划分算法和图重划分算法.首先介绍图划分的3种不同的划分策略及问题定义、图的两种不同的动态性来源以及动态图划分问题;然后介绍3种不同的流式图划分算法,包括基于Hash的划分算法、基于邻居分布的划分算法以及基于流的优化划分算法;其次介绍单元素增量式划分和批量增量式划分这两种不同的增量式图划分算法;再次,分别介绍针对图结构动态的重划分算法和针对图计算动态的重划分算法;最后,在对已有方法分析和比较的基础上,总结目前动态图划分面临的主要挑战,提出相应的研究问题.     

知识图谱划分算法研究综述

知识图谱是人工智能的重要基石,因其包含丰富的图结构和属性信息而受到广泛关注.知识图谱可以精确语义描述现实世界中的各种实体及其联系,其中顶点表示实体,边表示实体间的联系.知识图谱划分是大规模知识图谱分布式处理的首要工作,对知识图谱分布式存储、查询、推理和挖掘起基础支撑作用.随着知识图谱数据规模及分布式处理需求的不断增长,...     

基于启发策略的动态平衡图划分算法

随着计算技术的发展以及大数据时代的来临,分布式计算已成为研究的热点,其中大图迭代计算作为其研究的重点,降低划分后子图之间的通信边规模是改善计算性能的关键.传统算法很难在切割率最小化与负载均衡上同时满足.由于图划分属于NP组合优化问题,提出了一种动态平衡算法来解决图的平衡划分,确保在子图边界点划分最优的基础上引入扰动策略使其跳出局部最优扩大搜索空间,最后在真实世界图上验证算法的可行性,分别从平衡系数、切割边规模与传统算法进行了比较.在指定的扰动次数下,此算法比常见的算法hash,Chunk,Metis在割边率上分别降低了近40%,30%,5%.与Metis相比,平衡系数也更加地优化,实验结果证明了该算法的有效性.     

有向图并行计算中的多目标剖分算法

在以离散网格为基础的某些数值模拟中,网格间的数据依赖关系可以抽象为有向图．如何剖分这些有向图成多个子图,将各子图对应的数值模拟任务映射到不同的处理机,是该类数值模拟并行计算的基础．剖分算法中,需要综合考虑连通性、并行度、负载平衡、通信开销四个目标．文章在传统有向图剖分算法的基础上,提出了一个权衡这四个目标的有向图多目标剖分区域分解算法．应用于二维非结构网格上的柱对称中子输运并行计算中,通量扫描并行算法在该区域剖分算法上获得的并行效率比原来的无向图区域剖分算法高50％以上．     

Discrete and Continuous Models for Partitioning Problems

Recently, variational relaxation techniques for approximating solutions of partitioning problems on continuous image domains have received considerable attention, since they introduce significantly less artifacts than established graph cut-based techniques. This work is concerned with the sources of such artifacts. We discuss the importance of differentiating between artifacts caused by discretization and those caused by relaxation and provide supporting numerical examples. Moreover, we consider in depth the consequences of a recent theoretical result concerning the optimality of solutions obtained using a particular relaxation method. Since the employed regularizer is quite tight, the considered relaxation generally involves a large computational cost. We propose a method to significantly reduce these costs in a fully automatic way for a large class of metrics including tree metrics, thus generalizing a method recently proposed by Strekalovskiy and Cremers (IEEE conference on computer vision and pattern recognition, pp. 1905–1911, 2011).     

A Dynamic Diffusion Optimization Method for Irregular Finite Element Graph Partitioning

To efficiently execute a finite element application program on a distributed memory multicomputer, we need to distribute nodes of a finite element graph to processors of a distributed memory multicomputer as evenly as possible and minimize the communication cost of processors. This partitioning problem is known to be NP-complete. Therefore, many heuristics have been proposed to find satisfactory sub-optimal solutions. Based on these heuristics, many graph partitioners have been developed. Among them, Jostle, Metis, and Party are considered as the best graph partitioners available up-to-date. For these three graph partitioners, in order to minimize the total cut-edges, in general, they allow 3% to 5% load imbalance among processors. This is a tradeoff between the communication cost and the computation cost of the partitioning problem. In this paper, we propose an optimization method, the dynamic diffusion method (DDM), to balance the 3% to 5% load imbalance allowed by these three graph partitioners while minimizing the total cut-edges among partitioned modules. To evaluate the proposed method, we compare the performance of the dynamic diffusion method with the directed diffusion method and the multilevel diffusion method on an IBM SP2 parallel machine. Three 2D and two 3D irregular finite element graphs are used as test samples. For each test sample, 3% and 5% load imbalance situations are tested. From the experimental results, we have the following conclusions. (1) The dynamic diffusion method can improve the partition results of these three partitioners in terms of the total cut-edges and the execution time of a Laplace solver in most test cases while the directed diffusion method and the multilevel diffusion method may fail in many cases. (2) The optimization results of the dynamic diffusion method are better than those of the directed diffusion method and the multilevel diffusion method in terms of the total cut-edges and the execution time of a Laplace solver for most test cases. (3) The dynamic diffusion method can balance the load of processors for all test cases.