A parallel algorithm for the enumeration of the spanning trees of a graph

As is well known, the strategy of divide-and-conquer is widely used in problem solving. The method of partitioning is also a fundamental strategy for the design of a parallel algorithm. The problem of enumerating the spanning trees of a graph arises in several contexts such as computer-aided design and computer networks. A parallel algorithm for solving the problem is presented in this paper. It is based on the principle of the inclusion and exclusion of sets, and not directly based on the partitioning of the graph itself. The results of the preliminary experiments on a MIMD system appear promising.     

An effective and efficient parallel approach for random graph generation over GPUs

The widespread usage of random graphs   has been highlighted in the context of database applications for several years. This because such data structures turn out to be very useful in a large family of database applications ranging from simulation to sampling, from analysis of complex networks to study of randomized algorithms, and so forth. Amongst others, Erd?s–Rényi _Γv,p${\Gamma }_{v,p}$ is the most popular model to obtain and manipulate random graphs. Unfortunately, it has been demonstrated that classical algorithms for generating Erd?s–Rényi based random graphs do not scale well in large instances and, in addition to this, fail to make use of the parallel processing capabilities of modern hardware. Inspired by this main motivation, in this paper we propose and experimentally assess a novel parallel algorithm for generating random graphs under the Erd?s–Rényi model that is designed and implemented in a Graphics Processing Unit (GPU), called PPreZER. We demonstrate the nice amenities due to our solution via a succession of several intermediary algorithms, both sequential and parallel, which show the limitations of classical approaches and the benefits due to the PPreZER algorithm. Finally, our comprehensive experimental assessment and analysis brings to light a relevant average speedup gain of PPreZER over baseline algorithms.     

An efficient parallel graph edge matching algorithm and its applications

A fast and efficient parallel algorithm for finding a maximal edge matching in an undirected graphG(V,E) is proposed.It runs in O(log n)time with O(m,/log n n)processors on an EREW PRAM for a class of graph set П,where n=|V|,m=|E|and П includes at least (i)planar graphs;(ii) graphs of bounded genus;and (iii)graphs of bounded maximum degress and so on.Our algorithm improves the previously known best algorithms by a factor of logn in the time complexity with linear number of processors on EREW PRAMs when the input is limited to П.     

半监督免疫克隆选择图划分方法

在聚类过程中利用一定量先验信息会显著提高聚类算法的性能。为了解决求解图谱划分方法NP难的问题并合理地利用一定量的先验信息,将成对限制信息引入到图谱划分方法中样本点的相似性测度,并在获得的相应的相似性矩阵的基础上,利用免疫克隆选择优化方法来优化图谱划分准则,提出了半监督免疫克隆选择图划分方法。USPS手写体数字集和UMIST人脸数据集识别的仿真实验证明了新方法的有效性。     

A parallel median algorithm

We give a deterministic algorithm for finding the kth smallest item in a set of n items, running in O((log log n)²) parallel time on O(n) processors in Valiant's comparison model.     

基于并行图计算的社区划分方法

以图计算形式研究社交网络由来已久,但对于如何提升图计算应用于大规模社交网络的计算速度和扩展性,一直是研究的难点。谱图论的应用为社交网络在图计算方面的研究带来新的研究热点,谱图分割为社交网络社区划分带来基于结构的支撑。为了解决谱图论在处理大规模社交网络时存在计算缓慢、内存溢出等问题,本文提出了谱聚类改进算法结合矩阵方式在并行环境下的处理方法。首先,利用Spark对网络数据进行并行化预处理,将社交网络以图结构表示,再将图转化为Spark分布式稀疏矩阵。然后,将谱聚类改进算法在Spark环境下,实现并行化社交网络社区快速划分,并以分布式方式持久化存储源数据、中间计算数据和计算结果,提高图计算在社交网络中的可靠性。最后,通过实验证明并行化图计算方法能有效提高计算速度和扩展性,支持大规模社交网络的挖掘分析,实现并行算法下高并发、高吞吐的特点。     

构造对角Ramsey图的DNA算法设计*

Ramsey数问题是一个著名的组合优化问题, 同时也是一个NP完全问题。构造对角Ramsey图是一个难处理的计算问题,使用穷举的算法来构造对角Ramsey图必然导致计算量的指数爆炸,穷举的DNA算法也不例外。提出了一个构造对角Ramsey图的递阶式DNA粘贴—剪接算法,该算法通过逐个添加顶点的思想, 逐步删除了问题的绝大部分非解,在一定程度上缓解了问题解的空间扩散。特别地, 专门针对对角Ramsey数R(5,5)的43阶Ramsey图的构造问题进行了计算分析, 分析结果充分地肯定了该算法的有效性。     

基于图模型的多边形自动并行构建算法

目前GIS基础算法并行化成为高性能GIS进一步深入的前提,作为GIS空间分析基础算法的重点,有必要对多边形构建提出一种自动并行算法。为此,提出基于图模型的多边形自动并行构建算法。该算法根据图模型中有向闭合环的特点对一组线段的集合进行多边形构建,能有效提高多边形构建的自动化程度。将搜索、排序等耗时较多的操作进行并行化处理,能有效减少全局搜索次数及整体排序和逻辑操作时间。实验表明,在对大规模线性数据生成区域时,该算法能有效地实现效率提升,达到良好的效果。     

A nearly optimal deterministic parallel Voronoi diagram algorithm

We describe ann-processor,O(log(n) log log(n))-time CRCW algorithm to construct the Voronoi diagram for a set ofn point-sites in the plane.A preliminary version of this paper was presented at the 17th EATCS ICALP meeting at Warwick, England, in July 1990.Supported by the US NSF under Grants CCR 890221 and CCR 8906949.Supported by the US NSF under Grants CCR 8810568, CCR-9003299, and IRI-9116843, and by the NSF and DARPA under Grant CCR 8908092.Supported by the EU Esprit program under BRAs 3075 (ALCOM) and 7141 (ALCOM II).     

迭代的图变换匹配算法

目的：图像的精确匹配在图像处理与识别中起着重要的作用。为了提高图像的匹配效果,本文提出了一种迭代的图变换匹配算法来实现误匹配关系的去除从而提高图像的匹配精度。方法：该算法首先利用传统的图变换匹配(GTM)算法从初始匹配关系集合中获得较为精确的匹配关系子集,然后,利用已经获得的正确匹配点集与初始匹配点集之间的几何关系对初始匹配进行修正。最后,利用GTM对修正后的匹配关系进一步优化,从而得到更多的精确匹配关系。结果：实验结果显示在不同的图像变换场景下,相比于传统GTM算法,该算法具有较高的查全率。结论：所提算法能够克服传统GTM算法所得正确匹配关系少的缺陷。     

A parallel decoding algorithm for LZ2 data compression

The LZ2 compression method is hardly parallelizable since it is known to be P-complete. In spite of such negative result, we show in this paper that the decoding process can be parallelized efficiently on an EREW PRAM model of computation with O(n/log(n)) processors and O(log² n) time, where n is the length of the output string.     

A parametric filtering algorithm for the graph isomorphism problem

We introduce a new filtering algorithm, called IDL(d)-filtering, for a global constraint dedicated to the graph isomorphism problem—the goal of which is to decide if two given graphs have an identical structure. The basic idea of IDL(d)-filtering is to label every vertex with respect to its relationships with other vertices around it in the graph, and to use these labels to filter domains by removing values that have different labels. IDL(d)-filtering is parameterized by a positive integer value d which gives a limit on the distance between a vertex to be labelled and the set of vertices considered to build its label. We experimentally compare different instantiations of IDL(d)-filtering with state-of-the-art dedicated algorithms and show that IDL(d)-filtering is more efficient on regular sparse graphs and competitive on other kinds of graphs.     

面向图分割问题的确定性退火控制算法

图分割问题是一种典型的NP-hard 问题, 如何对其进行高效求解一直都是学界和工业界的一个难题. 本文构建了一种新型的确定性退火控制算法, 提供了图分割问题的一种高质量近似解法. 算法主要由两部分构成: 全局收敛的迭代过程以及屏障函数最小点组成的收敛路径. 我们证明了,当屏障因子从足够大的实数降为0, 沿着一系列由屏障问题最小点组成的收敛路径可以得到图分割问题的一种高质量的近似解. 仿真计算结果表明本文所构建算法相比已有方法的优越性     

A parallel algorithm solving a tridiagonal Toeplitz linear system

A new tridiagonal Toeplitz linear system (TTLS) solver is proposed. The solver first decomposes an n-dimensional strictly diagonally dominant TTLS equation into a number of m-dimensional subsystems employing a modified Gaussian elimination method. An analytic solution of a continued fraction is obtained to derive the solver. The solver based on the modified Gaussian elimination method fully exploits parallelism. Computation and communication complexities of the proposed algorithm are all shown to be O(n/m).     

Optimal parallel algorithm for findingst-ambitus of a planar biconnected graph

A cycleC passing through two specific verticess andt of a biconnected graph is said to be anst-ambitus if its bridges do not interlace in some special way. We present algorithms forst-ambitus for planar biconnected graphs, which are much simpler than the one known for general graphs [MT]. Our algorithm runs inO(n) time on a sequential machine and (logn) parallel time usingO(n/logn) processors on an EREW PRAM.     

A fast successive over-relaxation algorithm for force-directed network graph drawing

Force-directed approach is one of the most widely used methods in graph drawing research. There are two main problems with the traditional force-directed algorithms. First, there is no mature theory to ensure the convergence of iteration sequence used in the algorithm and further, it is hard to estimate the rate of convergence even if the convergence is satisfied. Second, the running time cost is increased intolerablely in drawing largescale graphs, and therefore the advantages of the force-directed approach are limited in practice. This paper is focused on these problems and presents a sufficient condition for ensuring the convergence of iterations. We then develop a practical heuristic algorithm for speeding up the iteration in force-directed approach using a successive over-relaxation (SOR) strategy. The results of computational tests on the several benchmark graph datasets used widely in graph drawing research show that our algorithm can dramatically improve the performance of force-directed approach by decreasing both the number of iterations and running time, and is 1.5 times faster than the latter on average.     

An efficient parallel algorithm for computing a large independent set in a planar graph

Let (G) denote the independence number of a graphG, that is the maximum number of pairwise independent vertices inG. We present a parallel algorithm that computes in a planar graphG = (V, E), an independent set such that ¦I¦ (G)/2. The algorithm runs in timeOlog² n) and requires a linear number of processors. This is achieved by denning a new set of reductions that can be executed locally and simultaneously; furthermore, it is shown that a constant fraction of the vertices in the graph are reducible. This is the best known approximation scheme when the number of processors available is linear; parallel implementation of known sequential algorithms requires many more processors.Joseph Naor was supported by Contract ONR N00014-88-K-0166. Most of this work was done while he was a post-doctoral fellow at the Department of Computer Science, University of Southern California, Los Angeles, CA 90089-0782, USA.