并行归并排序算法

构造效率为Ｏ（１）的并行算法是一个引人注目的问题。［１］和［２］分别提出了并行度为Ｏ（ｌｏｇｎ）和Ｏ（ｎ＾１／２）的、效率为Ｏ（１）的并行排序算法。本文提出一种新的并行排序算法，其效率为Ｏ（１），而并行步数小于［１］和［２］的算法的并行步数。经过改进后，在保持效率为Ｏ（１）的情况下，可进一步将并行度扩大到Ｏ（ｎ＾１／２ｌｏｇ ｎ）。     

可重构造的网孔机器上的k-选择

对于一个 ｍ ×ｎ（ｍ ≤ｋ）的列有序矩阵,文中在 ｎ × ｎ 可重构造的网孔机器上提出了一个并行 ｋ选择算法,其时间复杂度为 Ｏ（ｌｏｇ２ｍ ＋ ｌｏｇｍ ｌｏｇ２ ｎ＋ ｌｏｇ３ ｎ）,而对于一般的ｌ元集,文中在相同的模型下提出了一个时间复杂度为 Ｏ ｌｏｇ２ ｌｎ ＋ ｌｏｇ ｌｎ ｌｏｇ２ ｎ＋ ｌｏｇ３ｎ＋ ｌｎ ｌｏｇ ｌｎ 的并行 ｋ选择算法．当时 ｌ≥ Ｏ（ｎｌｏｇ３ｎ／ｌｏｇ ｌｏｇｎ,该时间复杂度为 Ｏ ｌｎ ｌｏｇ ｌｎ ．特别地,当ｌ＝ Ｏ（ｎ１＋ ε）（ε＞ ０ 为常数）,则时间复杂度为 Ｏ ｌｎ ｌｏｇｎ ．此时达到的加速比为 ｎ／ｌｏｇｎ．     

货郎担问题最优并行启发式算法

本文给出了满足三角不等式的货郎担问题的并行启发式算法，在ＳＩＭＤ ＣＲＥＶ ＰＲＡＭ并行机上该算法使用Ｏ（ｎ＾３／ｌｏｇ＾２ｎ）台处理器需Ｏ熄ｌｏｇ＾２ｎ）时间，这里ｎ是给定城市的个数，因而该并行算法是最优的。     

完全欧几里德距离变换的最优算法

欧几里德距离变换（ＥＤＴ）对由黑白素构成的二值图象中所有象素找出其到最近黑素的距离，应用于图象分析，计算机视觉，在本文之前，该问题的最好复杂度为Ｏ（ｎ＾２ｌｏｇｎ）。本文提出了一个复杂度为Ｏ（ｎ＾２）的算法，使复杂度达到最优，该算法可以并行化，在有ｒ个处理单元的ＥＲＥＷＰＲＡＭ计算模型上，若ｒｌｏｇｒ≤２２／６ｎ，则时间复杂度为Ｏ（ｎ／ｒ）否则为Ｏ（ｎｌｏｇｒ）。     

无存储器中冲突的并行快速排序算法

本文在一个ＥＲＥＷ ＰＲＡＭｅｘｃｌｕｓｉｖｅ ｒｅａｄ ｅｘｃｌｕｓｉｖｅ ｗｒｉｔｅ ｐａｒａｌｌｅｄ ｒａｎｄｏｍ ａｃｃｅｓｓ ｍａｃｈｉｎｅ）上提出一个并行快速排序算法，这个算法用Ｋ个处理器可将Ｎ个项目在平均Ｏ（ｎ／ｋ＋ｌｏｇｎ）ｌｏｇｎ）时间内排序，所以平均来说算法的时间和处理器数量的乘积对任何ｋ≤ｎ／ｌｏｇｎ是Ｏ（ｎｌｏｇｎ）。     

一个多元选择算法

本文基于数排序的思想，从高位关键字开始，对ｍ位关键字的ｎ个记录进行扫描，给出了一个多元选择算法，算法的最坏复杂度为Ｏ（ｍ（ｎ＋ｒ）），但平均复杂度为Ｏ（ｎ＋ｒ）。     

一类扩展的Steiner树优化问题及其应用

本文提出了一个计算机网络通信和分布式系统中的一类扩展的Ｓｔｅｉｎｅｒ树问题．对此问题设计了两个求其最优解的算法．这两个算法的时间复杂性分别是Ｏ（３（ｋ－１）·ｎ＋２（ｋ－１）·ｎ２）和Ｏ（２（ｎ－ｋ）·ｎ２）．其中，ｋ是一棵Ｓｔｅｉｎｅｒ树需支撑的给定顶点的个数．     

Toeplitz矩阵相乘的快速卷积算法

本文利用Ｔｏｅｐｌｉｔｚ矩阵可分解为循环阵与斜循环阵之和的特点２，借助于卷积的ＦＦＴ算法，推导出计算两个Ｔｏｅｐｌｉｔｚ矩阵之积的一种新的快速算法，其乘法复杂性为２ｎ＾２＋Ｏ（ｎｌｏｇ２ｎ）。     

最短路径树的计算与修改算法

在有向赋权图Ｇ＝（Ｖ，Ｅ，ＣＯＳＴ）上，给出了求解以每个顶点为根的向前／向后最短路径树（ＦＢＳＰＴ）算法。当Ｇ中的边被删除或边权增加时，证明了在这种情况下，不可能存在高效的对ＦＢＳＰＴ的修改算法；而对边添加和边权减少的情况，本文给出时间复杂性为Ｏ（ｎ￣２）的修改算法。此外，本文也讨论了对上述算法的并行实现问题。     

几何算法求解货郎担问题

本文提出求解货郎担问题的一种几何算法。它的时间复杂性为：Ｏ（ｎ＾３／ｍ）次比较，Ｏ（ｎ＾２）次乘法，其中ｎ，ｍ分别是点集的点数和凸包顶点数。     

线对象邻接关系快速重构算法

给定向量化坐标,计算n个线对象两两邻接关系,普通算法时间复杂度为O(n*n);理论最好时间复杂度为O(C),其中C是邻接关系的基数。基于散列桶,给出了建立线对象邻接关系的快速算法,其平均时间复杂度为O(n(1+1/r)),r为算法分配的桶数量与n的比,空间复杂度为O(n)。证明了若不允许使用额外空间,则不可能使用排序算法解决该问题;给出了允许使用额外空间条件下的两遍排序算法,时间复杂度为O(n(lbn+1+2/r))。应用表明快速算法比普通算法速度提高1~3个数量级。     

An O(n) algorithm for the linear multiple choice knapsack problem and related problems

We present an O(n) algorithm for the Linear Multiple Choice Knapsack Problem and its d-dimensional generalization which is based on Megiddo's (1982) algorithm for linear programming. We also consider a certain type of convex programming problems which are common in geometric location models. An application of the linear case is an O(n) algorithm for finding a least distance hyperplane in R^d according to the rectilinear norm. The best previously available algorithm for this problem was an O(n log²n) algorithm for the two-dimensional case. A simple application of the nonlinear case is an O(n) algorithm for finding the point at which a ‘pursuer’ minimizes its distance from the furthest among n ‘targets’, when the trajectories involved are straight lines in R^d.     

一种计算图像几何矩的快速算法

提出了一种计算图像几何矩的快速算法.根据图像区域边界的顶点链码,给出了图像几何矩的计算公式.该算法可以看作是格林理论的离散版本的一个推广,对低阶几何矩,算法的复杂度为O(n).与原有的几何矩算法比较,该方法具有实现简单、计算量小、计算结果精确等优点.     

Efficient EREW PRAM algorithms for parentheses-matching

We present four polylog-time parallel algorithms for matching parentheses on an exclusive-read and exclusive-write (EREW) parallel random-access machine (PRAM) model. These algorithms provide new insights into the parentheses-matching problem. The first algorithm has a time complexity of O(log² n) employing O(n/(log n)) processors for an input string containing n parentheses. Although this algorithm is not cost-optimal, it is extremely simple to implement. The remaining three algorithms, which are based on a different approach, achieve O(log n) time complexity in each case, and represent successive improvements. The second algorithm requires O(n) processors and working space, and it is comparable to the first algorithm in its ease of implementation. The third algorithm uses O(n/(log n)) processors and O(n log n) space. Thus, it is cost-optimal, but uses extra space compared to the standard stack-based sequential algorithm. The last algorithm reduces the space complexity to O(n) while maintaining the same processor and time complexities. Compared to other existing time-optimal algorithms for the parentheses-matching problem that either employ extensive pipelining or use linked lists and comparable data structures, and employ sorting or a linked list ranking algorithm as subroutines, the last two algorithms have two distinct advantages. First, these algorithms employ arrays as their basic data structures, and second, they do not use any pipelining, sorting, or linked list ranking algorithms     

深度优先稳定原地归并排序的高效算法

基于分治策略,使用深度优先的方法,提出了一种用于线性表的稳定原地归并排序算法,其时间复杂度为O(n lb n),辅助空间复杂度为O(1),递归栈空间复杂度为O(lb n),同时进行了算法分析和实验测试。实验结果表明,该算法效率较STL中的稳定原地归并排序算法有67.51%的提升,解决了稳定排序算法中要么时间复杂度高要么空间复杂度高的问题。     

An Optimal Parallel Co-Connectivity Algorithm

In this paper we consider the problem of computing the connected components of the complement of a given graph. We describe a simple sequential algorithm for this problem, which works on the input graph and not on its complement, and which for a graph on n vertices and m edges runs in optimal O(n+m) time. Moreover, unlike previous linear co-connectivity algorithms, this algorithm admits efficient parallelization, leading to an optimal O(log n)-time and O((n+m)log n)-processor algorithm on the EREW PRAM model of computation. It is worth noting that, for the related problem of computing the connected components of a graph, no optimal deterministic parallel algorithm is currently available. The co-connectivity algorithms find applications in a number of problems. In fact, we also include a parallel recognition algorithm for weakly triangulated graphs, which takes advantage of the parallel co-connectivity algorithm and achieves an O(log² n) time complexity using O((n+m²) log n) processors on the EREW PRAM model of computation.     

一种求简单多边形凸包的最优算法

计算一般多边形凸包的算法时间复杂度为Ｏ（ｎ＾２）。     

关于迷宫排序问题的研究

本文首先把迷宫排序问题推广为ｍ×ｎ迷宫（ｍ＞１，ｎ＞１）的排序问题，证明了ｍ×ｎ迷宫的任一初始状态能经过有限步移动转变成目标状态的充要条件，然后给出了一个ｍ×ｎ迷宫排序的算法，该算法的时间复杂度是Ｏ（ｍｎ（ｍ＋ｎ）），空间复杂度是Ｏ（ｍｎ）．最后还指出了它的时间复杂度的一个下界．这样，关于迷宫排序问题就基本上得到了圆满地解决．     

An Efficient Adaptive Algorithm for Constructing the Convex Differences Tree of a Simple Polygon

The convex differences tree (CDT) representation of a simple polygon is useful in computer graphics, computer vision, computer aided design and robotics. The root of the tree contains the convex hull of the polygon and there is a child node recursively representing every connectivity component of the set difference between the convex hull and the polygon. We give an O(n log K + K log² n) time algorithm for constructing the CDT, where n is the number of polygon vertices and K is the number of nodes in the CDT. The algorithm is adaptive to a complexity measure defined on its output while still being worst case efficient. For simply shaped polygons, where K is a constant, the algorithm is linear. In the worst case K = O(n) and the complexity is O(n log² n). We also give an O(n log n) algorithm which is an application of the recently introduced compact interval tree data structure.