重图的均匀边染色

图G的一个边染色称为是均匀的,如果对G的每个顶点v,与v关联的染任意两种颜色的边数至多相差一,我们给出了重图均匀边染色的一个充分条件。     

Edge-Coloring Bipartite Multigraphs in O(E logD) Time

Let V, E, and D denote the cardinality of the vertex set, the cardinality of the edge set, and the maximum degree of a bipartite multigraph G. We show that a minimal edge-coloring of G can be computed in O(E logD time. This result follows from an algorithm for finding a matching in a regular bipartite graph in O(E) time. Received September 23, 1999     

An Adaptive Parallel Tempering Algorithm

Parallel tempering is a generic Markov chain Monte Carlo sampling method which allows good mixing with multimodal target distributions, where conventional Metropolis-Hastings algorithms often fail. The mixing properties of the sampler depend strongly on the choice of tuning parameters, such as the temperature schedule and the proposal distribution used for local exploration. We propose an adaptive algorithm with fixed number of temperatures which tunes both the temperature schedule and the parameters of the random-walk Metropolis kernel automatically. We prove the convergence of the adaptation and a strong law of large numbers for the algorithm under general conditions. We also prove as a side result the geometric ergodicity of the parallel tempering algorithm. We illustrate the performance of our method with examples. Our empirical findings indicate that the algorithm can cope well with different kinds of scenarios without prior tuning. Supplementary materials including the proofs and the Matlab implementation are available online.     

改进伪并行遗传算法求解作业车间调度问题

针对遗传算法在求解极复杂优化问题中出现的过早收敛、执行效率差的缺点,提出了一种改进的伪并行遗传算法.该算法将并行进化与串行搜索相结合,提高了算法的收敛速度.同时该算法通过种群因子控制伪并行算法中的各子种群的规模,不仅保证了搜索过程中勘探和开采的平衡,克服过早收敛,而且减少了计算的复杂性,特别是在处理复杂优化问题上具有较高的性能.实验结果证明了该算法的有效性.     

一种迭代格式的有限元并行算法*

本文提出了一种求解有限元方程的迭代格式的并行算法.该方法在线性代数方程迭代解法的基础上,引进并行运算步骤;并且运用加权残数方法,通过选择适当的权函数,推导了该并行算法的有限元基本格式.该方法在西安交通大学BLXSI-6400并行计算机上程序实现.计算结果表明它能有效地提高运算速度,减少计算时间,是一种有效的求解大型结构有限元方程的并行算法.     

Cycle Frames of Complete Multipartite Multigraphs ‐ III

For two graphs G and H their wreath product has vertex set in which two vertices and are adjacent whenever or and . Clearly, , where is an independent set on n vertices, is isomorphic to the complete m‐partite graph in which each partite set has exactly n vertices. A 2‐regular subgraph of the complete multipartite graph containing vertices of all but one partite set is called partial 2‐factor. For an integer λ, denotes a graph G with uniform edge multiplicity λ. Let J be a set of integers. If can be partitioned into edge‐disjoint partial 2‐factors consisting cycles of lengths from J, then we say that has a ‐cycle frame. In this paper, we show that for and , there exists a ‐cycle frame of if and only if and . In fact our results completely solve the existence of a ‐cycle frame of .     

Multigraphs without large bonds are wqo by contraction

We show that the class of multigraphs with at most p connected components and bonds of size at most k is well‐quasi‐ordered by edge contraction for all positive integers . (A bond is a minimal nonempty edge cut.) We also characterize canonical antichains for this relation.     

Optimal Edge-Colourings for a Class of Planar Multigraphs

  Let G be a multigraph containing no minor isomorphic to or (where denotes without one of its edges). We show that the chromatic index of G is given by , where is the maximum valency of G and is defined as

Interval Non‐edge‐Colorable Bipartite Graphs and Multigraphs

An edge‐coloring of a graph G with colors is called an interval t‐coloring if all colors are used, and the colors of edges incident to any vertex of G are distinct and form an interval of integers. In 1991, Erd?s constructed a bipartite graph with 27 vertices and maximum degree 13 that has no interval coloring. Erd?s's counterexample is the smallest (in a sense of maximum degree) known bipartite graph that is not interval colorable. On the other hand, in 1992, Hansen showed that all bipartite graphs with maximum degree at most 3 have an interval coloring. In this article, we give some methods for constructing of interval non‐edge‐colorable bipartite graphs. In particular, by these methods, we construct three bipartite graphs that have no interval coloring, contain 20, 19, 21 vertices and have maximum degree 11, 12, 13, respectively. This partially answers a question that arose in [T.R. Jensen, B. Toft, Graph coloring problems, Wiley Interscience Series in Discrete Mathematics and Optimization, 1995, p. 204]. We also consider similar problems for bipartite multigraphs.     

FGFT的并行算法及其应用

常见的离散Fourier变换(DFT)的推广均定义在一个交换环上。我们在[1]、[2]中给出了DFT在一类非交换环上的推广(FGFT),并将它应用于一些快速线性计算问题。本文将不加证明地列出这些快速算法的并行计算效率。结果表明,这些计算问题亦具有很好的并行性。     

A Parallel Algorithm for Toeplitz Triangular Matrices

A new parallel algorithm for inverting Toeplitz triangular matrices as well as solving Toeplitz triangular linear systems is presented in this paper. The algorithm possesses very good parallelism, which can easily be adjusted to match the natural hardware parallelism of the computer systems, that was assumed to be much smaller than the order $n$ of the matrices to be considered since this is the usual case in practical applications. The parallel time complexity of the algorithm is $O([n/p|\log n+\log^2p)$, where $p$ is the hardware parallelism.     

A Randomized Parallel Algorithm for Planar Graph Isomorphism

We present a parallel randomized algorithm running on aCRCW PRAM, to determine whether two planar graphs are isomorphic, and if so to find the isomorphism. We assume that we have a tree of separators for each planar graph (which can be computed by known algorithms inO(log² n) time withn^{1 + ε}processors, for any ε > 0). Ifnis the number of vertices, our algorithm takesO(log(n)) time with processors and with a probability of failure of 1/nat most. The algorithm needs 2 · log(m) − log(n) + O(log(n)) random bits. The number of random bits can be decreased toO(log(n)) by increasing the number of processors ton^{3/2 + ε}, for any ε > 0. Our parallel algorithm has significantly improved processor efficiency, compared to the previous logarithmic time parallel algorithm of Miller and Reif (Siam J. Comput.20(1991), 1128–1147), which requiresn⁴randomized processors orn⁵deterministic processors.     

A Parallel Algorithm for Multiple Objective Linear Programs

This paper presents an ADBASE-based parallel algorithm forsolving multiple objective linear programs (MOLPs). Job balance,speedup and scalability are of primary interest in evaluatingefficiency of the new algorithm. The scalability of a parallelalgorithm is a measure of its capacity to increase performance withrespect to the number of processors used. Implementation results onIntel iPSC/2 and Paragon multiprocessors show that the algorithmsignificantly speeds up the process of solving MOLPs, which isunderstood as generating all or some efficient extreme points andunbounded efficient edges. The algorithm is shown to be scalable andgives better results for large problems. Motivation andjustification for solving large MOLPs are also included.     

A Randomized Parallel Algorithm for Single-Source Shortest Paths

We give a randomized parallel algorithm for computing single-source shortest paths in weighted digraphs. We show that the exact shortest-path problem can be efficiently reduced to solving a series of approximate shortest-path subproblems. Our algorithm for the approximate shortest-path problem is based on the technique used by Ullman and Yannakakis in a parallel algorithm for breadth-first search.     

A Parallel Algorithm for Computing Minimum Spanning Trees

present a simple and implementable algorithm that computes a minimum spanning tree of an undirected weighted graph G = (V, E) of n = |V| vertices and m = |E| edges on an EREW PRAM in O(log^3/2n) time using n + m processors. This represents a substantial improvement in the running time over the previous results for this problem using at the same time the weakest of the PRAM models. It also implies the existence of algorithms having the same complexity bounds for the EREW PRAM, for connectivity, ear decomposition, biconnectivity, strong orientation, st-numbering and Euler tours problems.     

A Parallel Algorithm for Large-Scale Nonconvex Penalized Quantile Regression

Penalized quantile regression (PQR) provides a useful tool for analyzing high-dimensional data with heterogeneity. However, its computation is challenging due to the nonsmoothness and (sometimes) the nonconvexity of the objective function. An iterative coordinate descent algorithm (QICD) was recently proposed to solve PQR with nonconvex penalty. The QICD significantly improves the computational speed but requires a double-loop. In this article, we propose an alternative algorithm based on the alternating direction method of multiplier (ADMM). By writing the PQR into a special ADMM form, we can solve the iterations exactly without using coordinate descent. This results in a new single-loop algorithm, which we refer to as the QPADM algorithm. The QPADM demonstrates favorable performance in both computational speed and statistical accuracy, particularly when the sample size n and/or the number of features p are large. Supplementary material for this article is available online.     

并行加工系统中的一种排序算法

通过对现有单机和相同机组并行加工系统排序问题的研究，建立了一类多机非相同机组并行加工系统的排序模型，模型的优化目标是工件排序的拖期总数为极小。由于已经证明它是一个NP问题，本提出了一个针对该问题的快速、实用的启发式排序算法，并用实例说明了算法的有效性。     

线性互补问题的并行多分裂松弛迭代算法

运用矩阵多重分裂理论,同时考虑并行计算与松弛迭代法,得到一类求解线性互补问题的高效数值算法．当问题的系数矩阵为对角元为正的H-矩阵或对称半正定矩阵时,证明了算法的全局收敛性；该算法与已有算法相比,具有计算量小、计算速度快等特点,因而特别适于求解大规模问题．数值试验的结果说明了算法的有效性．     

Parallel Algorithm for Unconstrained Optimization Based on Decomposition Techniques

We present a numerical implementation of the parallel gradient distribution (PGD) method for the solution of large-scale unconstrained optimization problems. The proposed parallel algorithm is characterized by a parallel phase which exploits the portions of the gradient of the objective function assigned to each processor; then, a coordination phase follows which, by a synchronous interaction scheme, optimizes over the partial results obtained by the parallel phase. The parallel and coordination phases are implemented using a quasi-Newton limited-memory BFGS approach. The computational experiments, carried out on a network of UNIX workstations by using the parallel software tool PVM, show that parallelization efficiency was problem dependent and ranged between 0.15 and 8.75. For the 150 problems solved by PGD on more than one processor, 85 cases had parallelization efficiency below 1, while 65 cases had a parallelization efficiency above 1.     

An Accurate Distance Algorithm for Octree‐Encoded Objects

Distance algorithms are most frequently used in robotics to determine the distance between two obstacles in the environment of a robot or between a sensor point and an object. Bounding volumes are a common technique; this technique relies on a hierarchical model representation of the two surfaces using axis‐aligned bounding boxes. Formoving objects it is interesting to use unaligned octrees to avoid the wrapping effect that occurs when performing octree decomposition in a common coordinate system after several rotations. We discuss the algorithm for computing accurate enclosures for the distance between objects represented by axis‐aligned or unaligned octrees. This algorithm is based on a new, recently published distance algorithm between two objects represented by axis‐aligned octrees. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)