一个选择算法及其并行化

文中用合并选择的思想及堆上的最佳算法，给出了求解选择问题的一个新算法及其相应的并行化。将串行合并选择算法的复杂度ｎＬｏｇｋ＋Ｏ（ｎ）降低到（ｎＬｏｇｋ）／２＋（ｎＬｏｇＬｏｇｋ）／２＋Ｏ（ｎ），并保持了原并行算法的结构，在ＳＩＭＤ树型机器的并行计算模型上，并行运行     

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．     

最小生成树的高效异步并行算法

在ＭＩＭＤ－ＳＭ并行计算模型上，本文给出了时间复杂性为Ｏ（ｎ（ｎ／ｐ＋ｌｏｇｐ））的最小生成树的异步并行算法，其中ｎ，ｐ（１≤ｐ≤ｎ）分别表示图的顶点数和处理机的个数。     

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。     

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）。     

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．     

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．     

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）。     

求解最优二分搜索树

最优二分搜索树的求解在一些实际问题中是经常碰到的，本文首先对该问题以及已有的几种求解算法作一介绍和评述，之后给出求解ＯＢＳＴ的更优算法，以及其正确性证明和算法评价。该算法的时间复杂度为最好的结果９。     

一种基于二叉树结构表达的二维实体布局算法

利用二叉树表达二维实体布局问题,得到一个完全自动的二维实体布局算法,算法的复杂性为Ｏ（ｎ）,其中ｎ是区域树的结点数,提出了区域树面积因子等新概念,给出一个精美的旋转区域树的方法,证明了若干基本定理。     

A fast dot-product algorithm with minimal rounding errors

We present a new algorithm which computes dot-products of arbitrary length with minimal rounding errors, independent of the number of addends. The algorithm has anO(n) time andO(1) memory complexity and does not need extensions of the arithmetic kernel, i.e, usual floating-point operations. A slight modification yields an algorithm which computes the dot-product in machine precision. Due to its simplicity, the algorithm can easily be implemented in hardware.     

机器人路径规划中的双向Dijkstra二叉树算法

在分析现有路径规划和碰撞检测方法的基础上,提出了一种新的机器人路径规划方法：双向Dijkstra二叉树算法。在机器人路径规划中应用传统的Dijkstra算法时间复杂度是O(n¬¬¬¬2),应用该文提出的算法进行路径规划的时间复杂度为O(nlog2n)。通过一些数据的检测,验证了在机器人路径规划中,尤其是在测试数据较多的情况下,该算法可以有效提高效率。     

Design and Performance Evaluation of Sequence Partition Algorithms

Tradeoffs between time complexities and solution optimalities are important when selecting algorithms for an NP-hard problem in different applications. Also, the distinction between theoretical upper bound and actual solution optimality for realistic instances of an NP-hard problem is a factor in selecting algorithms in practice. We consider the problem of partitioning a sequence of n distinct numbers into minimum number of monotone （increasing or decreasing） subsequences. This problem is NP-hard and the number of monotone subsequences can reach [√2n＋1/1-1/2]in the worst case. We introduce a new algorithm, the modified version of the Yehuda-Fogel algorithm, that computes a solution of no more than [√2n＋1/1-1/2]monotone subsequences in O（n^1.5） time. Then we perform a comparative experimental study on three algorithms, a known approximation algorithm of approximation ratio 1.71 and time complexity O（n^3）, a known greedy algorithm of time complexity O（n^1.5 log n）, and our new modified Yehuda-Fogel algorithm. Our results show that the solutions computed by the greedy algorithm and the modified Yehuda-Fogel algorithm are close to that computed by the approximation algorithm even though the theoretical worst-case error bounds of these two algorithms are not proved to be within a constant time of the optimal solution. Our study indicates that for practical use the greedy algorithm and the modified Yehuda-Fogel algorithm can be good choices if the running time is a major concern.     

基于自适应搜索窗口的序列相似比对算法

DTW（Dynamic Time Warping）算法被广泛应用于序列数据比对,以度量序列间距离,但算法较高的时间复杂度限制了其在长序列比对上的应用。提出基于自适应搜索窗口的序列相似比对算法（ADTW）,算法利用分段聚集平均（Piecewise Aggregate Approximation,PAA）策略进行序列抽样得到低精度序列,然后计算低精度序列下的比对路径,并根据低精度距离矩阵上的梯度变化预测路径偏差,限制路径搜索窗口的拓展范围;随后算法逐步提高序列精度,并在搜索窗口内修正路径、计算新的搜索窗口,最终,实现DTW距离和相似比对路径的快速求解。对比FastDTW,ADTW算法在同等度量准确率下提高计算效率约20%,其时间复杂度为[O(n)]。     

A Randomized Parallel Three-Dimensional Convex Hull Algorithm for Coarse-Grained Multicomputers

We present a randomized parallel algorithm for constructing the three-dimensional convex hull on a generic p-processor coarse-grained multicomputer with arbitrary interconnection network and n/p local memory per processor, where n/p ≥ p ^2+ε (for some arbitrarily small ε > 0). For any given set of n points in 3-space, the algorithm computes the three-dimensional convex hull, with high probability, in local computation time and O(1) communication phases with at most O(n/p) data sent/received by each processor. That is, with high probability, the algorithm computes the three-dimensional convex hull of an arbitrary point set in time , where Γ _n,p denotes the time complexity of one communication phase. The assumption n/p ≥ p ^2+ε implies a coarse-grained, limited parallelism, model which is applicable to most commercially available multiprocessors. In the terminology of the BSP model, our algorithm requires, with high probability, O(1) supersteps, synchronization period , computation cost , and communication cost O((n/p) g). Received October 30, 1995, and in revised form April 15, 1996, and in final form September 17, 1996.     

A Flexible Algorithm for Generating All the Spanning Trees in Undirected Graphs

In this paper we propose an algorithm for generating all the spanning trees in undirected graphs. The algorithm requires O (n+m+ τ n) time where the given graph has n vertices, m edges, and τ spanning trees. For outputting all the spanning trees explicitly, this time complexity is optimal. Our algorithm follows a special rooted tree structure on the skeleton graph of the spanning tree polytope. The rule by which the rooted tree structure is traversed is irrelevant to the time complexity. In this sense, our algorithm is flexible. If we employ the depth-first search rule, we can save the memory requirement to O (n+m). A breadth-first implementation requires as much as O (m+ τ n) space, but when a parallel computer is available, this might have an advantage. When a given graph is weighted, the best-first search rule provides a ranking algorithm for the minimum spanning tree problem. The ranking algorithm requires O (n+ m + τ n) time and O (m+ τ n) space when we have a minimum spanning tree. Received January 21, 1995; revised February 19, 1996.     

Engineering the Divide-and-Conquer Closest Pair Algorithm

We improve the famous divide-and-conquer algorithm by Bentley and Shamos for the planar closest-pair problem. For n points on the plane, our algorithm keeps the optimal O（n log n） time complexity and, using a circle-packing property, computes at most 7n/2 Euclidean distances, which improves Ge et al.＇s bound of （3n log n）/2 Euclidean distances. We present experimental results of our comparative studies on four different versions of the divide-and-conquer closest pair algorithm and propose two effective heuristics.     

A linear time algorithm for computing exact Euclidean distance transforms of binary images in arbitrary dimensions

A sequential algorithm is presented for computing the exact Euclidean distance transform (DT) of a k-dimensional binary image in time linear in the total number of voxels N. The algorithm, which is based on dimensionality reduction and partial Voronoi diagram construction, can be used for computing the DT for a wide class of distance functions, including the L/sub p/ and chamfer metrics. At each dimension level, the DT is computed by constructing the intersection of the Voronoi diagram whose sites are the feature voxels with each row of the image. This construction is performed efficiently by using the DT in the next lower dimension. The correctness and linear time complexity are demonstrated analytically and verified experimentally. The algorithm may be of practical value since it is relatively simple and easy to implement and it is relatively fast (not only does it run in O(N) time but the time constant is small). A simple modification of the algorithm computes the weighted Euclidean DT, which is useful for images with anisotropic voxel dimensions. A parallel version of the algorithm runs in O(N/p) time with p processors.     

数据包过滤规则的快速匹配算法和冲突检测

通过分析数据包过滤技术中的性能瓶颈,提出了过滤规则的快速匹配算法BSLT．该算法采用Trie数据结构存储规则表,并只在叶节点存储相应规则,节省了存储空间,其空间复杂度为O(NW),查找的时间复杂度为O(W);在匹配时采用二分法进行查找,提高了匹配速度,匹配的时间复杂度为O(N)．实验证明BSLT的吞吐率在100条规则内比顺序匹配算法提高了近20％,而且规则越多．BSLT的优势越明显．此外,分析了数据包过滤技术的另一个问题——规则冲突,给出了冲突的理论证明和查找算法．实验证明该算法能准确地检测出冲突规则．     

基于八叉树的三维地质剖面生成算法

针对目前构建三维地质剖面算法复杂度高、效率低的问题,提出一种基于八叉树的三维地质剖面生成算法。利用八叉树算法对传统的地质剖面生成算法进行改进,使算法在搜索过程中的时间复杂度降低至O(log8(n/M)),在算法中加入轮廓边约束,对搜索到的边进行预处理,以保证边的正确性和有序性。采用八叉树为复杂三维地质体网格模型内的三角形创建空间索引,通过八叉树快速查找出经过剖面的三角形,计算交点并追踪出轮廓边界,通过画廊看守算法对追踪出的边界三角化并构建三维剖面。实验结果表明,该算法具有复杂度低、鲁棒性强的特点,与传统的地质剖面生成算法相比,时间复杂度由O(n2)降低到O(nlbn)。