Multisets排序的最优并行算法

排序是一个既有十分重要的理论意义又有广泛的实际应用价值的问题 ,其中 ,Multisets排序问题是指对只有k个不同关键字值的n个数据 (记录 )进行排序 ,0 相似文献   

虫孔路由二维网孔机器上的最优图论算法

连通分量和最小生成树是图论中的两个基本问题 ,在许多领域都有很多应用 .对于顶点数为 n的图和规模为 p× p的虫孔路由二维网孔机器 ,该文针对 p n和 n

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并行双调排序算法的有效实现及性能分析

排序是计算机中最常见的操作之一，双调排序是一个非常著名的排离算法，也是最早的并行排序算法，又调排离对排序算法的研究具有非常深远的影响，基于双调排序算法的基本思想，介绍了双调排序在分布存储的并行计算机环境下的一种有效实现方式，采用局部多对多通信替换全局通信，很好地解决了双调排序中的通信问题，算法的计算复杂度为⊙n/p(logn log^2p)，其中n为待排序的关键字个数,p为处理器数，算法在二维网孔结构上通信时间复杂度达到了O（2.12132√p.n/p）其量级达到了理论上的下限，分析结果表明，双调排序算法也具有很好的通信性能和可扩展性。     

一种适用于多处理机系统的并行排序方法DCPM

本文给出一种适用于多处理器系统的并行排序方法——PCPM(Divide Conquer Parallel Merge)。证明了该方法的正确性;算出了它的时间复杂度为0(n~(1/2) log n~(1/2) log√n);最后,简单地说明了本方法的特点。     

关于RSA加密方法不动点的注记

设n=P1P2……Pk,其中诸pi是互不相同的素数,e是满足（e,φ（n))=1的整数,φn)=(p1-1)…（Pk-1),以RSA（n,e)表示以n和e为公开钥的RSA公钥加密体制,利用孙子定理,给出院 计算RSA（n,e)的与n互素的a阶不动点的方法,以T（n,e,a)表示这个加密体制的与n互素的a阶不动点的个数,记S（n,e,K)=Ⅱa=1^kT(n,e,a)^1/k,则logS(n,e,K)=ωn)log2 1/K∑p/n∑q/p-1∑r^m|plogr[K(indge,r^m-1(r-1))/r^m-1(r-1)]。     

基于二叉树的反向Hash链遍历

提出了一种反向Hash链遍历的时间、空间复杂度优化算法.采用堆栈操作实现了高效的反向Hash链遍历,并将Hash链遍历过程映射到了二叉树的后序遍历过程,利用二叉树性质对存储和计算性能进行了理论化分析和证明.分析证明结果表明,遍历对长为n的反向Hash链时,算法只需要存储[lbn]+1个节点值,并且进行不多于[(lbn-/2+1)n次Hash计算次数.相比同类其他算法,该算法并不要求链长为2的整数次方.通过对算法进行基于k叉树(k≥3)的扩展,进一步将存储空间降低到[lo gk[(k-1)n+1],但总计算次数提高到[(-logk[(k-1)n+1]-1)k/2+1]n;通过在算法执行前先把Hash链平分为p段(p≥2),将总计算次数降低到[(lb(n/p)-/2+1)n,但是所需的存储空间提高到[(lb(n/p)+1)p.     

按位链接快速排序算法

提出了一种对任意整数都适用的按位链接快速排序算法，其时间复杂性为O（n)，只需附加2n 10k（其中k为待排序数组最大数的位数）个存储空间。     

改进的赫夫曼树（Huffman Tree）和赫夫曼编码（Huffman Code）构造算法

通过将待排序的数据应用快速排序算法进行排序处理,使得赫夫曼算法（Huffman Algorithm）65时间复杂度从O（n^2）降低为O（n＊log2n）。当用于构造赫夫曼树（Huffman Tree）的结点比较多时,可较大的提高程序的运行时间。     

A Unified O(log N) and Optimal Sorting Vector Algorithm

A unified vector sorting algorithm(VSA) is proposed,which sorts N arbitrary numbers with c log2 N-bits on an SIMD multi-processor system (SMMP) with p=N^1 ε/u processors and a composite interconnected network in T=c/ε(4 log2 N-2 log2 u 10u) time,where c is an arbitrary positive constant.When ε is an arbitrary small positive constant and u=log2 N,it is an O(log N) algorithm and p=N^1 ε/log2 N;when ε=1/log N and u=2 log2 N,it is an optimal algorithm (p=N/log2 N,T=O(log^2 N),pT=O(N log N));where u=1,c=1 and ε=0.5 (a constant).     

FlashSort排序解法及实现

现在最快的排序算法是快速排序算法,它的时间复杂度达到O(n log n)。但是还有一种排序算法,就是Flashsort排序算法。它的时间复杂度达到O(n),超过了前者。FlashSort排序是基于分类的算法,它的实现思想很简单,是利用构造出来的索引来排序。举一个简单的例子,比如有一百个整数,你很容易就能把它们放在数组的正确位置上,根本不需要作任何比较。     

Multiway merging in parallel

The problem of merging k (k⩾2) sorted lists is considered. We give an optimal parallel algorithm which takes O((n log k/p)+log n) time using p processors on a parallel random access machine that allows concurrent reads and exclusive writes, where n is the total size of the input lists. This algorithm achieves O(log n) time using p=n log k/log n processors. Most of the previous log n research for this problem has been focused on the case when k=2. Very recently, parallel solutions for the case when k=2 have been reported. Our solution is the first logarithmic time optimal parallel algorithm for the problem when k⩾2. It can also be seen as a unified optimal parallel algorithm for sorting and merging. In order to support the algorithm, a new processor assignment strategy is also presented     

Finding a Region with the Minimum Total L 1 Distance from Prescribed Terminals

Given k terminals and n axis-parallel rectangular obstacles on the plane, our algorithm finds a plane region R* such that, for any point p in R*, the total length of the k shortest rectilinear paths connecting p and the k terminals without passing through any obstacle is minimum. The algorithm is output-sensitive, and takes O((K+n) log n) time and O(K+n) space if k is a fixed constant, where K is the total number of polygonal vertices of the found region R*.     

Free binary decision diagrams for the computation of EAR n

Free binary decision diagrams (FBDDs) are graph-based data structures representing Boolean functions with the constraint (additional to binary decision diagram) that each variable is tested at most once during the computation. The function EAR_n is the following Boolean function defined for n × n Boolean matrices: EAR_n(M) = 1 iff the matrix M contains two equal adjacent rows. We prove that each FBDD computing EAR_n has size at least and we present a construction of such diagrams of size approximately .     

Energy-efficient permutation routing in radio networks

A radio network (RN, for short) is a distributed system populated by small, hand-held commodity devices running on batteries. Since recharging batteries may not be possible while on mission, we are interested in designing protocols that are highly energy efficient. One of the most effective energy-saving strategies is to mandate that the stations go to sleep whenever they do not transmit or receive messages. It is well known that a station is expending power while its transceiver is active, that is, while transmitting or receiving a packet. It is perhaps surprising at first that a station is expending power even if it receives a packet that is not destined for it. Since, in single-hop radio networks, every station is within transmission range from every other station, the design of energy-efficient protocols is highly nontrivial. An instance of the permutation routing problem involves p stations of an RN, each storing n/p items. Each item has a unique destination which is the identity of the station to which the item must be routed. The goal is to route all the items to their destinations while expending as little energy as possible. Since, in the worst case, each item must be transmitted at least once, every permutation routing protocol must take n/k time slots. Similarly, each station must be awake for at least n/p time slots to transmit and/or receive packets. Our main contribution is to present an almost optimal energy-efficient permutation routing protocol for a k-channel, a p-station RN that routes n packets in at most (2d+2b+1)n/k+k time slots with no station being awake for more than (4d+7b-1)n/p time slots, where d=[(logp/k)/(logn/p)], b=[(log k)/(logn/p)] and k⩽√(p/2). Since, in most real-life situations, the number n of packets to route, the number p of stations in the RN, and the number k of channels available satisfy the relation k≪p≪n, it follows that d and b are very small     

Work-time optimal k-merge algorithms on the PRAM

For 2⩽k⩽n, the k-merge problem is to merge a collection of ksorted sequences of total length n into a new sorted sequence. The k-merge problem is fundamental as it provides a common generalization of both merging and sorting. The main contribution of this work is to give simple and intuitive work-time optimal algorithms for the k-merge problem on three PRAM models, thus settling the status of the k-merge problem. We first prove that Ω(n log k) work is required to solve the k-merge problem on the PRAM models. We then show that the EREW-PRAM and both the CREW-PRAM and the CRCW require Ω(log n) time and Ω(log log n+log k) time, respectively, provided that the amount of work is bounded by O(n log k). Our first k-merge algorithm runs in Θ(log n) time and performs Θ(n log k) work on the EREW-PRAM. Finally, we design a work-time optimal CREW-PRAM k-merge algorithm that runs in Θ(log log n+log k) time and performs Θ(n log k) work. This latter algorithm is also work-time optimal on the CREW-PRAM model. Our algorithms completely settle the status of the k-merge problem on the three main PRAM models     

Branch-and-bound and backtrack search on mesh-connected arrays of processors

In this paper we investigate the parallel complexity of backtrack and branch-and-bound search on the mesh-connected array. We present an (dN/logdN) lower bound for the time needed by arandomized algorithm to perform backtrack and branch-and-bound search of a tree of depthd on the N × N mesh, even when the depth of the tree is known in advance. The lower bound also holds for algorithms that are allowed to move tree-nodes and create multiple copies of the same tree-node.For the upper bounds we givedeterministic algorithms that are within a factor of 0(log^3/2 N) from our lower bound. Our algorithms do not make any assumption on the shape of the tree to be searched, do not know the depth of the tree in advance, and do not move tree-nodes nor create multiple copies of the same node.The best previously known algorithm for backtrack search on the mesh was randomized and required (dN/ logN) time. Our algorithm for branch-and-bound is the first algorithm that performs branch-and-bound search on a sparse network. Both the lower and the upper bounds extend to meshes of higher dimensions.Part of this work was done while the authors were at Harvard University.     

The mixing properties of certain processes related to Markov chains

Summary Let {Y _n ,– < n < } be either a function of a stationary Markov chain with countable state space, or a finitary process in the sense of Heller [3]. The purpose of this note is to prove that if {Y _n ,– < n < } is mixing, then it is aK-shift. (Definitions will be given below.)IfT is a measure-preserving transformation on a probability space, then the following implications relevant to the present paper are known: (1)T is aK-shift T is (r + 1)-mixing T isr-mixing T is totally ergodic T is ergodic, and (2)T is ergodic T is totally ergodic T isr-mixing T is aK-shift.It is not known if the classes ofr-mixing and (r + 1)-mixing transformations are distinct. (1-mixing is also called mixing.) The results of this note then imply that for the classes of transformation that we are consideringr-mixing and (r + 1)-mixing are equivalent.This research was partially supported by NSF Grant GP-19660.