基于谱方法的无向赋权图剖分算法*

在多水平方法初始剖分阶段提出了一种基于谱方法的无向赋权图剖分算法SPWUG,给出了基于Lanczos迭代计算Laplacian矩阵次小特征值及特征向量的实现细节。SPWUG算法借助Laplacian矩阵次小特征值对应的特征向量,刻画了节点间相对距离,将基于非赋权无向图的Laplacian谱理论在图的剖分应用方面扩展到无向赋权图上,实现了对最小图的初始剖分。基于ISPD98电路测试基准的实验表明,SPWUG算法取得了一定性能的改进。实验分析反映了在多水平方法中,最小图上的全局近似最优剖分可能是初始图的局部最     

Path-distance heuristics for the Steiner problem in undirected networks

An integrative overview of the algorithmic characteristics of three well-known polynomialtime heuristics for the undirected Steiner minimum tree problem:shortest path heuristic (SPH),distance network heuristic (DNH), andaverage distance heuristic (ADH) is given. The performance of thesesingle-pass heuristics (and some variants) is compared and contrasted with several heuristics based onrepetitive applications of the SPH. It is shown that two of these repetitive SPH variants generate solutions that in general are better than solutions obtained by any single-pass heuristic. The worst-case time complexity of the two new variants isO(pn ³) andO(p ³ n ²), while the worst-case time complexity of the SPH, DNH, and ADH is respectivelyO(pn ²),O(m + n logn), andO(n ³) wherep is the number of vertices to be spanned,n is the total number of vertices, andm is the total number of edges. However, use of few simple tests is shown to provide large reductions of problem instances (both in terms of vertices and in term of edges). As a consequence, a substantial speed-up is obtained so that the repetitive variants are also competitive with respect to running times.     

对数空间可构造的无向图遍历序列

研究了为无向连通子图设计环状遍历序列（TSC）的空间复杂性问题。通过定义对数空间的Cook归约,分析了TSC问题与无向图连接性问题及通用遍历序列构造问题的关系,证明了TSC问题以及无向图遍历问题是对数空间可解的,并给出了一个TSC一般性构造方法。最后还提出了一个更有效的针对树状图的TSC构造算法。     

Efficient approximation algorithms for shortest cycles in undirected graphs

We describe a simple combinatorial approximation algorithm for finding a shortest (simple) cycle in an undirected graph. Given an adjacency-list representation of an undirected graph G with n vertices and unknown girth k, our algorithm returns with high probability a cycle of length at most 2k for even k and 2k+2 for odd k, in time . Thus, in general, it yields a approximation. For a weighted, undirected graph, with non-negative edge weights in the range {1,2,…,M}, we present a simple combinatorial 2-approximation algorithm for a minimum weight (simple) cycle that runs in time O(n²logn(logn+logM)).     

Searching for optimal integer solutions to set partitioning problems using column generation

In this paper, we describe a new approach to increase the possibility of finding integer feasible columns to a set partitioning problem (SPP) directly in solving the linear programming (LP) relaxation using column generation. Traditionally, column generation is aimed to solve the LP‐relaxation as quickly as possible without any concern for the integer properties of the columns formed. In our approach, we aim to generate columns forming an optimal integer solution while simultaneously solving the LP‐relaxation. Using this approach, we can improve the possibility of finding integer solutions by heuristics at each node in the branch‐and‐bound search. In addition, we improve the possibility of finding high‐quality integer solutions in cases where only the columns in the root node are used to solve the problem. The basis of our approach is a subgradient technique applied to a Lagrangian dual formulation of the SPP extended with an additional surrogate constraint. This extra constraint is not relaxed and is used to better control the subgradient evaluations and how the multiplier values are computed. The column generation is then directed, via the multipliers, to construct columns that form feasible integer solutions. Computational experiments show that we can generate optimal integer columns in a large set of well‐known test problems as compared to both standard and stabilized column generation, and simultaneously keep the number of columns smaller than standard column generation. This is also supported by tests on a case study with work‐shift generation.     

面向SoC的系统级并行划分方法

为缩短复杂SoC系统的设计周期,降低系统设计的复杂性,提出了一种SoC系统级的并行划分方法.引入带有信号激活率和输入输出延时的过程模型图,为SoC系统构建模型.设计一启发式算法对该过程模型图进行并行划分,同时,该算法能解决有环图的划分问题.通过大量的实验证明,划分结果同要求吻合,说明该划分方法是可行、有效的.     

Missing data imputation, matching and other applications of random recursive partitioning

Applications of the random recursive partitioning (RRP) method are described. This method generates a proximity matrix which can be used in non-parametric matching problems such as hot-deck missing data imputation and average treatment effect estimation. RRP is a Monte Carlo procedure that randomly generates non-empty recursive partitions of the data and calculates the proximity between observations as the empirical frequency in the same cell of these random partitions over all the replications. Also, the method in the presence of missing data is invariant under monotonic transformations of the data but no other formal properties of the method are known yet. Therefore, Monte Carlo experiments were conducted in order to explore the performance of the method. A companion software is available as a package for the R statistical environment.     

Improved algorithms for recognizing p-Helly and hereditary p-Helly hypergraphs

A hypergraph H is set of vertices V together with a collection of nonempty subsets of it, called the hyperedges of H. A partial hypergraph of H is a hypergraph whose hyperedges are all hyperedges of H, whereas for V^′⊆V the subhypergraph (induced by V^′) is a hypergraph with vertices V^′ and having as hyperedges the subsets obtained as nonempty intersections of V^′ and each of the hyperedges of H. For p?1 say that H is p-intersecting when every subset formed by p hyperedges of H contain a common vertex. Say that H is p-Helly when every p-intersecting partial hypergraph H^′ of H contains a vertex belonging to all the hyperedges of H^′. A hypergraph is hereditary p-Helly when every (induced) subhypergraph of it is p-Helly. In this paper we describe new characterizations for hereditary p-Helly hypergraphs and discuss the recognition problems for both p-Helly and hereditary p-Helly hypergraphs. The proposed algorithms improve the complexity of the existing recognition algorithms.     

网络中最短距离的递归算法

提出了在搜索过程中采用标记最短距离,调用递归函数用回溯搜索法求解网络最短距离的算法。该算法可以方便地求解复杂网络或复杂迷宫的通道与最短距离问题,在求解结果中给出从起点到网络通道上任意点的路径标识和最短距离值等信息,在无向加权图的最短路径求解中,显示出比Dijkstra方法小的时间复杂度。该算法克服了传统回溯法求解复杂迷宫时被时间复杂度和空间复杂度困扰的难题,显示出良好的应用前景。     

Cost-driven vertical class partitioning for methods in object oriented databases

In object-oriented databases (OODBs), a method encapsulated in a class typically accesses a few, but not all the instance variables defined in the class. It may thus be preferable to vertically partition the class for reducing irrelevant data (instance variables) accessed by the methods. Our prior work has shown that vertical class partitioning can result in a substantial decrease in the total number of disk accesses incurred for executing a set of applications, but coming up with an optimal vertical class partitioning scheme is a hard problem. In this paper, we present two algorithms for deriving optimal and near-optimal vertical class partitioning schemes. The cost-driven algorithm provides the optimal vertical class partitioning schemes by enumerating, exhaustively, all the schemes and calculating the number of disk accesses required to execute a given set of applications. For this, a cost model for executing a set of methods in an OODB system is developed. Since exhaustive enumeration is costly and only works for classes with a small number of instance variables, a hill-climbing heuristic algorithm (HCHA) is developed, which takes the solution provided by the affinity-based algorithm and improves it, thereby further reducing the total number of disk accesses incurred. We show that the HCHA algorithm provides a reasonable near-optimal vertical class partitioning scheme for executing a given set of applications.Received: 29 March 1999, Accepted: 11 March 2002, Published online: 3 April 2003This research has been supported, in part, by Hong Kong UGC Research Grants Council under grant CityU 733/96E and CityU 1119/99E.     

基于数据流图的异构VLIW DSP分簇方法

超长指令字数字信号处理器(VLIW DSP)的指令级并行性(ILP)主要通过指令分簇和软件流水来实现。在以前的研究中,指令分簇主要只考虑指令级并行性和减少簇间转移指令,对异构体系结构和某些寄存器只能分在指定簇上的情况考虑较少。提出一种基于数据流图(DFG)的异构体系结构上的分簇方法,利用指令的相关性将DFG划分为与簇数目相同个数的子图,再根据特殊寄存器对簇的要求采用启发式算法对子图进行调整,实验结果表明这种分簇方法使得负载更均衡,加速比相对于传统方法可以提高8%左右。     

改进的二维增强贪婪软硬件划分算法

针对嵌入式系统中的单处理器和单ASIC体系结构,将软硬件划分问题抽象为MKP模型,通过扩展其边界的维数,引入二维的贪婪算法来解决软硬件划分问题。算法旨在满足硬件面积约束、功耗约束和存储空间需求约束的前提下使系统的运行时间最优,算法的时间复杂度降低到O（log n·log n）。算法基于代表功能块粒度的控制数据流图（CFG）,摒弃了传统的面向软件或硬件的方法,给出了一种新的选择初始状态的方法,该方法将关键节点映射到软件,其余的用硬件实现,因缩小了算法的搜索空间,从而进一步提高了算法的运行速度。最后进行对比实验,实验结果证明该算法在运行时间和稳定性方面均优于遗传算法和模拟算法。     

Memory-based adaptive partitioning (MAP) of search space for the enhancement of convergence in Pareto-based multi-objective evolutionary algorithms

A new algorithm, dubbed memory-based adaptive partitioning (MAP) of search space, which is intended to provide a better accuracy/speed ratio in the convergence of multi-objective evolutionary algorithms (MOEAs) is presented in this work. This algorithm works by performing an adaptive-probabilistic refinement of the search space, with no aggregation in objective space. This work investigated the integration of MAP within the state-of-the-art fast and elitist non-dominated sorting genetic algorithm (NSGAII). Considerable improvements in convergence were achieved, in terms of both speed and accuracy. Results are provided for several commonly used constrained and unconstrained benchmark problems, and comparisons are made with standalone NSGAII and hybrid NSGAII-efficient local search (eLS).     

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.     

Clustering spatial networks for aggregate query processing: A hypergraph approach

In spatial networks, clustering adjacent data to disk pages is highly likely to reduce the number of disk page accesses made by the aggregate network operations during query processing. For this purpose, different techniques based on the clustering graph model are proposed in the literature. In this work, we show that the state-of-the-art clustering graph model is not able to correctly capture the disk access costs of aggregate network operations. Moreover, we propose a novel clustering hypergraph model that correctly captures the disk access costs of these operations. The proposed model aims to minimize the total number of disk page accesses in aggregate network operations. Based on this model, we further propose two adaptive recursive bipartitioning schemes to reduce the number of allocated disk pages while trying to minimize the number of disk page accesses. We evaluate our clustering hypergraph model and recursive bipartitioning schemes on a wide range of road network datasets. The results of the conducted experiments show that the proposed model is quite effective in reducing the number of disk accesses incurred by the network operations.     

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.     

Vertical partitioning for flash and HDD database systems

Recent advances in flash memory technology have greatly enhanced the capability of flash memory to address the I/O bottleneck problem. Flash memory has exceptional I/O performance compared to the hard disk drive (HDD). The superiority of flash memory is especially visible when dealing with random read patterns. Even though the cost of flash memory is higher than that of HDD storage, the popularity of flash memory is increasing at such a pace that it is becoming a common addition to the average computer. Recently, flash memory has been made into larger devices called solid state drives (SSDs). Although these devices can offer capacities comparable to HDDs, they are considerably more expensive per byte.Our research aims to increase the I/O performance of database systems by using a small amount of flash memory alongside HDD storage. The system uses a fully vertically partitioned storage structure where each column is stored separately on either the HDD or SSD. Our approach is to assign the columns into the SSD which will benefit the most from the characteristics of flash memory. We prove this problem is NP-complete and propose an optimal dynamic programming solution and a faster greedy heuristic solution.A system simulator has been implemented and experiments show that the overall I/O costs can be greatly reduced using only a limited amount of flash memory. The results show the greedy heuristic solution performed similarly to the more expensive dynamic programming solution for the situations tested.     

One-dimensional partitioning for heterogeneous systems: Theory and practice

We study the problem of one-dimensional partitioning of nonuniform workload arrays, with optimal load balancing for heterogeneous systems. We look at two cases: chain-on-chain partitioning, where the order of the processors is specified, and chain partitioning, where processor permutation is allowed. We present polynomial time algorithms to solve the chain-on-chain partitioning problem optimally, while we prove that the chain partitioning problem is NP-complete. Our empirical studies show that our proposed exact algorithms produce substantially better results than heuristics, while solution times remain comparable.     

RDF partitioning for scalable SPARQL query processing

The volume of RDF data increases dramatically within recent years, while cloud computing platforms like Hadoop are supposed to be a good choice for processing queries over huge data sets for their wonderful scalability. Previous work on evaluating SPARQL queries with Hadoop mainly focus on reducing the number of joins through careful split of HDFS files and algorithms for generating Map/Reduce jobs. However, the way of partitioning RDF data could also affect system performance. Specifically, a good partitioning solution would greatly reduce or even totally avoid cross-node joins, and significantly cut down the cost in query evaluation. Based on HadoopDB, this work processes SPARQL queries in a hybrid architecture, where Map/Reduce takes charge of the computing tasks, and RDF query engines like RDF-3X store the data and execute join operations. According to the analysis of query workloads, this work proposes a novel algorithm for automatically partitioning RDF data and an approximate solution to physically place the partitions in order to reduce data redundancy. It also discusses how to make a good trade-off between query evaluation efficiency and data redundancy. All of these proposed approaches have been evaluated by extensive experiments over large RDF data sets.     

A computational study of several relocation methods for k-means algorithms

The core of a k-means algorithm is the reallocation phase. A variety of schemes have been suggested for moving entities from one cluster to another and each of them may give a different clustering even though the data set is the same. The present paper describes shortcomings and relative merits of 17 relocation methods in connection with randomly generated data sets.