An Efficient Parallel Algorithm for the Layered Planar Monotone Circuit Value Problem

A planar monotone circuit (PMC) is a Boolean circuit that can be embedded in the plane and that contains only AND and OR gates. A layered PMC is a PMC in which all input nodes are in the external face, and the gates can be assigned to layers in such a way that every wire goes between gates in successive layers. Goldschlager, Cook and Dymond, and others have developed NC ² algorithms to evaluate a layered PMC when the output node is in the same face as the input nodes. These algorithms require a large number of processors (Ω(n ⁶ ), where n is the size of the input circuit). In this paper we give an efficient parallel algorithm that evaluates a layered PMC of size n in time using only a linear number of processors on an EREW PRAM. Our parallel algorithm is the best possible to within a polylog factor, and is a substantial improvement over the earlier algorithms for the problem. Received April 18, 1994; revised April 7, 1995.     

Parallel Algorithms for the Edge-Coloring and Edge-Coloring Update Problems

LetG(V,E) be a simple undirected graph with a maximum vertex degree Δ(G) (or Δ for short), |V| =nand |E| =m. An edge-coloring ofGis an assignment to each edge inGa color such that all edges sharing a common vertex have different colors. The minimum number of colors needed is denoted by χ′(G) (called thechromatic index). For a simple graphG, it is known that Δ ≤ χ′(G) ≤ Δ + 1. This paper studies two edge-coloring problems. The first problem is to perform edge-coloring for an existing edge-colored graphGwith Δ + 1 colors stemming from the addition of a new vertex intoG. The proposed parallel algorithm for this problem runs inO(Δ^3/2log³Δ + Δ logn) time usingO(max{nΔ, Δ³}) processors. The second problem is to color the edges of a given uncolored graphGwith Δ + 1 colors. For this problem, our first parallel algorithm requiresO(Δ^5.5log³Δ logn+ Δ⁵log⁴n) time andO(max{n²Δ,nΔ³}) processors, which is a slight improvement on the algorithm by H. J. Karloff and D. B. Shmoys [J. Algorithms8 (1987), 39–52]. Their algorithm costsO(Δ⁶log⁴n) time andO(n²Δ) processors if we use the fastest known algorithm for finding maximal independent sets by M. Goldberg and T. Spencer [SIAM J. Discrete Math.2 (1989), 322–328]. Our second algorithm requiresO(Δ^4.5log³Δ logn+ Δ⁴log⁴n) time andO(max{n²,nΔ³}) processors. Finally, we present our third algorithm by incorporating the second algorithm as a subroutine. This algorithm requiresO(Δ^3.5log³Δ logn+ Δ³log⁴n) time andO(max{n²log Δ,nΔ³}) processors, which improves, by anO(Δ^2.5) factor in time, on Karloff and Shmoys' algorithm. All of these algorithms run in the COMMON CRCW PRAM model.     

约束满足问题并行弧相容算法

本文给出了约束满足问题网络弧相容的两个并行算法ＰＡＣ－１和ＰＡＣ－２。     

A Survey of Parallel and Distributed Algorithms for the Steiner Tree Problem

Given a set of input points, the Steiner Tree Problem (STP) is to find a minimum-length tree that connects the input points, where it is possible to add new points to minimize the length of the tree. Solving the STP is of great importance since it is one of the fundamental problems in network design, very large scale integration routing, multicast routing, wire length estimation, computational biology, and many other areas. However, the STP is NP-hard, which shatters any hopes of finding a polynomial-time algorithm to solve the problem exactly. This is why the majority of research has looked at finding efficient heuristic algorithms. Additionally, many authors focused their work on utilizing the ever-increasing computational power and developed many parallel and distributed methods for solving the problem. In this way we are able to obtain better results in less time than ever before. Here, we present a survey of the parallel and distributed methods for solving the STP and discuss some of their applications.     

MIMD并行机上解决矩阵链乘序问题的算法研究

介绍了并行机向MIMD的发展趋势,描述了MIMD并行机上解决矩阵链乘序问题的算法,并对其复杂度进行了分析.针对处理器之间任务分配的问题,提出了一种合理分配任务的算法,并对这种算法的复杂度进行了分析.     

Selection Algorithms for Parallel Disk Systems

With the widening gap between processor speeds and disk access speeds, the I/O bottleneck has become critical. Parallel disk systems have been introduced to alleviate this bottleneck. In this paper we present deterministic and randomized selection algorithms for parallel disk systems. The algorithms to be presented, in addition to being asymptotically optimal, have small underlying constants in their time bounds and hence have the potential of being practical.     

Memetic Algorithms for Parallel Code Optimization

Discovering the optimum number of processors and the distribution of data on distributed memory parallel computers for a given algorithm is a demanding task. A memetic algorithm (MA) is proposed here to find the best number of processors and the best data distribution method to be used for each stage of a parallel program. Steady state memetic algorithm is compared with transgenerational memetic algorithm using different crossover operators and hill-climbing methods. A self-adaptive MA is also implemented, based on a multimeme strategy. All the experiments are carried out on computationally intensive, communication intensive, and mixed problem instances. The MA performs successfully for the illustrative problem instances.     

离散Fourier变换并行算法综述

本文详细介绍了1－D DFT精确计算的六步框架并行算法和按位并行计算法,以及按位计算法在2－D Mesh和Torus上的模拟实现,同时介绍了近似计算中的基于奇异值分解的算法和基于快速多极方法的算法。对于2－D DFT,本文介绍了并行行列算法和并行多项式变换算法,并分析了其优缺点。     

Scalable Parallel Algorithms for FPT Problems

Algorithmic methods based on the theory of fixed-parameter tractability are combined with powerful computational platforms to launch systematic attacks on combinatorial problems of significance. As a case study, optimal solutions to very large instances of the NP-hard vertex cover problem are computed. To accomplish this, an efficient sequential algorithm and various forms of parallel algorithms are devised, implemented, and compared. The importance of maintaining a balanced decomposition of the search space is shown to be critical to achieving scalability. Target problems need only be amenable to reduction and decomposition. Applications in high throughput computational biology are also discussed.     

Parallel Algorithms for Large-scale Nonlinear Optimization

Multi-step, multi-directional parallel variable metric (PVM) methods for unconstrained optimization problems are presented in this paper. These algorithms generate several VM directions at each iteration, dierent line search and scaling strategies are then applied in parallel along each search direction. In comparison to some serial VM methods, computational results show that a reduction of 200% or more in terms of number of iterations and function/gradient evaluations respectively could be achieved by the new parallel algorithm over a wide range of 63 test problems. In particular, when the complexity, or the size of the problem increases, greater savings could be achieved by the proposed parallel algorithm. In fact, the speedup factors gained by our PVM algorithms could be as high as 28 times for some test problems.     

Parallel Algorithms for Maximal Acyclic Sets

Given a graph G=(V,E), the well-known spanning forest problem of G can be viewed as the problem of finding a maximal subset F of edges in G such that the subgraph induced by F is acyclic. Although this problem has well-known efficient NC algorithms, its vertex counterpart, the problem of finding a maximal subset U of vertices in G such that the subgraph induced by U is acyclic, has not been shown to be in NC (or even in RNC) and is not believed to be parallelizable in general. In this paper we present NC algorithms for solving the latter problem for two special cases. First, we show that, for a planar graph with n vertices, the problem can be solved in time with O(n) processors on an EREW PRAM. Second, we show that the problem is solvable in NC if the input graph G has only vertex-induced paths of length polylogarithmic in the number of vertices of G. As a consequence of this result, we show that certain natural extensions of the well-studied maximal independent set problem remain solvable in NC. Moreover, we show that, for a constant-degree graph with n vertices, the problem can be solved in time with O(n ² ) processors on an EREW PRAM. Received July 3, 1995; revised April 1, 1996.     

Efficient Parallel Algorithms for Planar st-Graphs

Planar st -graphs find applications in a number of areas. In this paper we present efficient parallel algorithms for solving several fundamental problems on planar st -graphs. The problems we consider include all-pairs shortest paths in weighted planar st -graphs, single-source shortest paths in weighted planar layered digraphs (which can be reduced to single-source shortest paths in certain special planar st -graphs), and depth-first search in planar st -graphs. Our parallel shortest path techniques exploit the specific geometric and graphic structures of planar st -graphs, and involve schemes for partitioning planar st -graphs into subgraphs in a way that ensures that the resulting path length matrices have a monotonicity property [1], [2]. The parallel algorithms we obtain are a considerable improvement over the previously best known solutions (when they are applied to these st -graph problems), and are in fact relatively simple. The parallel computational models we use are the CREW PRAM and EREW PRAM.     

Optimal Parallel Algorithms for Quadtree Problems

In this paper we describe optimal processor-time parallel algorithms for set operations such as union, intersection, comparison on quadtrees. The algorithms presented in this paper run in O(log N) time using N/log N processors on a shared memory model of computation that allows concurrent reads or writes. Consequently they allow us to achieve optimal speedups using any number of processors up to N/log N. The approach can also be used to derive optimal processor-time parallel algorithms for weaker models of parallel computation.     

Efficient Parallel Algorithms for Permutation Graphs

In this paper, we present optimal O(log n) time, O(n/log n) processor EREW PRAM parallel algorithms for finding the connected components, cut vertices, and bridges of a permutation graph. We also present an O(log n) time, O(n) processor, CREW PRAM model parallel algorithm for finding a Breadth First Search (BFS) spanning tree of a permutation graph rooted at vertex 1 and use the same to derive an efficient parallel algorithm for the All Pairs Shortest Path problem on permutation graphs.     

起节点上并行算法设计策略的研究

本文分析了超节点这一新型体系结构上的算法设计方法,并具体讨论了超节点上的数据分配和任务划分,最后举出一个实例－－高斯消去法的分块算法,提出了如何在现有共享算法和分布算法的基础上,开发超节点上的并行算法。     

求解CARP-RP-ML问题的改进算法

传统方法无法有效求解交通道路维护运作中的有补给点及多装载的容量约束弧路径(CARP-RP-ML)问题。为此,提出改进的启发式算法和遗传算法。启发式算法将不同的分割算法用于由所有需求弧随机排序得到的个体上,构造问题的可行解;遗传算法利用分割算法计算其个体适应值,确定对应的可行车辆路径及补给位置,并用局部搜索作为变异算子,进一步扩大搜索空间。数值实验结果表明,与启发式算法相比,遗传算法能更有效地求解CARP-RP-ML问题。     

并行数据库上的并行CMD_Join算法

并行数据库在多处理机之间的分布方法(简称数据分布方法)对并行数据操作算法的性能影响很大.如果在设计并行数据操作算法时充分利用数据分布方法的特点,可以得到十分有效的并行算法.本文研究如何充分利用数据分布方法的特点,设计并行数据操作算法的问题,提出了基于CMD多维数据分布方法的并行CMD_Join算法.理论分析和实验结果表明,并行CMD_Join算法的效率高于其它并行Join算法.     

Algorithms for the Homogeneous Set Sandwich Problem

A homogeneous set is a non-trivial module of a graph, i.e. a non-empty, non-unitary, proper subset of a graph's vertices such that all its elements present exactly the same outer neighborhood. Given two graphs the Homogeneous Set Sandwich Problem (HSSP) asks whether there exists a sandwich graph which has a homogeneous set. In 2001 Tang et al. published an all-fast algorithm which was recently proven wrong, so that the HSSP's known upper bound would have been reset thereafter at the former determined by Cerioli et al. in 1998. We present, notwithstanding, new deterministic algorithms which have it established at We give as well two even faster randomized algorithms, whose simplicity might lend them didactic usefulness. We believe that, besides providing efficient easy-to-implement procedures to solve it, the study of these new approaches allows a fairly thorough understanding of the problem.