一类扩展的Steiner树优化问题有其应用

本文提出了一个计算机通信和分布式系统的一类扩展的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和Ｏ。其中，ｋ是一棵Ｓｔｅｉｎｅｒ树需支撑的给定顶点的个数。     

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．     

基于Wormhole路由的二维Mesh上的并行k-选择

由于二维网孔机器的结构简单、规整,易于ＶＬＳＩ实现,使得它不仅成为许多理论研究的基础模型,而且还是许多并行机所采用的互连结构．Ｗｏｒｍ ｈｏｌｅ 路由技术的采用改进了二维网孔机器的通信能力．该文在带有Ｗｏｒｍ ｈｏｌｅ 路由技术的ｎ×ｎ 二维网孔机器上提出了一个时间复杂度为Ｏ（ｌｏｇ２ｎｌｏｇｌｏｇｎ）的并行ｋ－选择算法,改进了该问题在Ｓｔｏｒｅ－ａｎｄ－Ｆｏｒｗ ａｒｄ 路由技术下的时间复杂度下界Ｏ（ｎ）．据已掌握的资料,该算法为最早的、非总线连接的二维网孔机器上的、时间复杂度为对数的多项式级的ｋ－选择算法．     

超立方网络上的平行路径

超立方是分布存储系中最常用的结构。在以往的工作中,人们已经提出了不少容错寻径算法,然而,还没有考虑Ｈｎ中│Ｆ│≥２ｎ－２的情形,在一个含有故障结点集Ｆ的ｎ维超立方网络Ｈｎ中,│Ｆ│≤４ｎ－２４,（ｓ０,ｄ０）,（ｓ１,ｄ１）是其中任意两对非故障结点,结果,（１）对↓Ａｖ∈Ｖ（Ｈｎ）,有│Ａ（ｖ,Ｈｎ－Ｆ）│≥６．（２）沿着某一维ｋ（０≤ｋ≤ｎ－１）,可将Ｈｎ分割成两部分：（ｄ０∈）Ｈｎ－１,０和（     

0-1背包问题的深度优先算法

本文介绍了０－１背包问题的一种深度优先（ＤＦＳ）算法,并用概率分析方法给出了算法的时间复杂度和空间复杂度,一般情况下,其时间复杂度在Ｏ（ｎ）到Ｏ（１．５）之间。工程管理上的一类整数规划问题都可归结为０．１背包问题。     

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．     

关于非对称线性方程组的新迭代算法

５１．引言 二阶椭圆型非对称方程是一类重要的科学工程计算的数学模型,如对流扩散和油藏模拟方程等,有着广泛的实际应用背景．文献［２］和［３］基于原始微分方程及对应的离散问题提出了正定可对称化的新概念．基于这一概念及文山我们研究针对二维和三维二阶常系数非对称椭圆型方程数值模型的新选代算法,首先考虑下面的一维椭圆型问题：对区间［０,１］均匀剖分后得ｎ＋２节点,即ｘ;一ｉ·ｈ;ｉ＝０,··,,ｎ＋１,其中ｈ＝／（＋１）．如果用中心差分格式离散方程（１．１）,则在节点Ｘ;有如下差分方程： 一（１＋ｗＮ。;－…     

二维模式近似匹配的快速算法

给定一个大小为ｎ×ｎ的文本Ｔ和一个大小为ｍ×ｍ的模板Ｐ，如果文本Ｔ中存在一个ｍ×ｍ的子块与模板Ｐ能够逐点匹配，称为精确匹配。如果最多有ｋ个元素不同，称为带有最多ｋ个误差的近似匹配。对于精确匹配，本文给出了一个时间复杂性为Ｏ（ｎ２ｌｏｇ｜∑｜）的算法，∑＝｛ａ１，２，…，ａ｜∑｜｝，是模板的字符集。对于近似匹配，快速算法分为两步：（１）预选。利用精确匹配算法找出能精确匹配的ｓ×ｓ（０≤ｓ≤ｍ）子块，得到ｈ个候选的对准点；（２）验证。把模板对准候选点，逐点比较，以确定不相同的元素是否不超过ｋ个。近似匹配的时间复杂性为Ｏ（ｎ２ｌｏｇ｜∑｜＋ｈｍ２）。     

N-Star网络中最优的点到多点平行路由算法

Ｃｈｅｎｔ等研究了ｎ－Ｓｔａｒ网络中的点到多点并行路由问题,对前人的工作做了很大的改进,给出了一个几乎最优的时间复杂度为Ｏ（ｎ＾２）的算法,由Ｃｈｅｎ的算法所给出的ｎ－１条路Ｐ２,…,Ｐｎ满足│Ｐｉ│≤ｄｉｓｔ（ｖ１,ｖｉ）＋６,其中Ｐｉ是连续ｖｉ到ｖ１的路,│Ｐｉ│表示路Ｐｉ的长度,ｄｉｓｔ（ｖ１,ｖｉ）表示ｖｉ到ｖ１的最短路的长度。     

环境因素对番茄单叶净光合速率的影响

论述了环境与番茄净光合速率间的关系及番茄净光合速率的日变化规律，在日光温室番茄光饱和点和补偿点范围内的光 光合曲线呈直角双曲线型，光饱和点为１３６１．４９μｍｏｌ·ｓ－１·ｍ－２，光补偿点为３７．０５μｍｏｌ·ｓ－１·ｍ－２，最大净光速率为１７．７０ｍｇＣＯ２·ｄｍ－２·ｈ－１。番茄在７～５０℃之间均有净光合，其温度 光合曲线呈抛物线型，且光合作用适宜温度范围为２４～３４℃，最适温度为２６～３２℃。光照度在１０２３．７５μｍｏｌ·ｓ－１·ｍ－２时，ＣＯ２饱和点为１９２５μＬ·Ｌ－１；光照度在５２６．５μｍｏｌ·ｓ－１·ｍ－２时，ＣＯ２饱和点为１７１８μＬ·Ｌ－１；光照度在３１２μｍｏｌ·ｓ－１·ｍ－２时，ＣＯ２饱和点为１７２１μＬ·Ｌ－１，但ＣＯ２补偿点为５７．１～７１．７μＬ·Ｌ－１，不同光照度间差异不大。番茄净光合速率日变化呈双峰曲线，但中午时的“午体现象”不明显。在正常的生产条件下，ＣＯ２浓度乃是经常的限制因子。因此，生产上人工施用ＣＯ２对提高番茄产量具有重要意义。     

Ad hoc网络时延受限的Steiner树启发式算法

针对Ad hoc网络时延受限的Steiner树问题,设计一个分布式的快速启发式算法DCST,该算法通过对网络中节点进行标号,并根据标号修改节点间的关联关系,建立一棵时延受限的Steiner树。在网络节点保持时间同步的前提下,算法的时间复杂度为O(n)。与现有经典的Steiner树算法相比,该算法具有明显优势。     

Minimum Connected Dominating Set Using a Collaborative Cover Heuristic for Ad Hoc Sensor Networks

A minimum connected dominating set (MCDS) is used as virtual backbone for efficient routing and broadcasting in ad hoc sensor networks. The minimum CDS problem is NP-complete even in unit disk graphs. Many heuristics-based distributed approximation algorithms for MCDS problems are reported and the best known performance ratio has (4.8+ln 5). We propose a new heuristic called collaborative cover using two principles: 1) domatic number of a connected graph is at least two and 2) optimal substructure defined as subset of independent dominator preferably with a common connector. We obtain a partial Steiner tree during the construction of the independent set (dominators). A final postprocessing step identifies the Steiner nodes in the formation of Steiner tree for the independent set of G. We show that our collaborative cover heuristics are better than degree-based heuristics in identifying independent set and Steiner tree. While our distributed approximation CDS algorithm achieves the performance ratio of (4.8+ln 5){rm opt} + 1.2, where {rm opt} is the size of any optimal CDS, we also show that the collaborative cover heuristic is able to give a marginally better bound when the distribution of sensor nodes is uniform permitting identification of the optimal substructures. We show that the message complexity of our algorithm is O(nDelta^{2} ), Delta being the maximum degree of a node in graph and the time complexity is O(n).     

Manhattan空间有障碍的最短路径和3-Steiner树算法

在VLSI设计中,多点互连是物理设计阶段的关键问题之一,而互连的点数等于2或大于2分别对应于Manhattan空间上有障碍时的最短路径问题和最小Steiner树问题,显然前者是后者的基础.连接图是研究最短路径问题的有效工具,已有的典型连接图包括基于轨迹的GC和GT以及基于自由区的GF和GG.工作包括3个方面:设计并分析了在各种连接图上实现动态的点对之间的最短路径查询算法;分析了在各个连接图上构造3-Steiner树的算法,对于已有的GC上的3-Steiner算法,将其Steiner顶点的候选集合规模从O((e+p)2)降低到了O((t+p)2),其中e,t,p分别表示边数、障碍极边数和顶点数;设计了在GG上的3-Steiner树构造算法,其平均情况时间复杂度只有(θ)(t).     

On approximation algorithms for the terminal Steiner tree problem

The terminal Steiner tree problem is a special version of the Steiner tree problem, where a Steiner minimum tree has to be found in which all terminals are leaves. We prove that no polynomial time approximation algorithm for the terminal Steiner tree problem can achieve an approximation ratio less than (1−o(1))lnn unless NP has slightly superpolynomial time algorithms. Moreover, we present a polynomial time approximation algorithm for the metric version of this problem with a performance ratio of 2ρ, where ρ denotes the best known approximation ratio for the Steiner tree problem. This improves the previously best known approximation ratio for the metric terminal Steiner tree problem of ρ+2.     

Optimal Sequential And Parallel Algorithms To Compute A Steiner Tree On Permutation Graphs

This paper presents an optimal sequential and an optimal parallel algorithm to compute a minimum cardinality Steiner set and a Steiner tree. The sequential algorithm takes O ( n ) time and parallel algorithm takes O (log n ) time and O ( n /log n ) processors on an EREW PRAM model.     

最多叶子生成树问题的核化算法

对算法领域的最多叶子生成树问题进行了深入研究,提出了对简单连通图2度节点的化简规则,并证明了不含2度节点的图的生成树的叶子节点数的下限为(N+6)/4,给出了构造这样一棵生成树的构造性方法.基于上述化简规则和所证明的结论,给出了最多叶子生成树问题的核化算法,该核化算法可以在O(n2)时间内得到一个4k-6大小的线性核.对于这样一个较小的核,将大大提高相关的参数算法和近似算法的性能.     

Concatenation-Based Greedy Heuristics for the Euclidean Steiner Tree Problem

We present a class of O(n log n) heuristics for the Steiner tree problem in the Euclidean plane. These heuristics identify a small number of subsets with few, geometrically close, terminals using minimum spanning trees and other well-known structures from computational geometry: Delaunay triangulations, Gabriel graphs, relative neighborhood graphs, and higher-order Voronoi diagrams. Full Steiner trees of all these subsets are sorted according to some appropriately chosen measure of quality. A tree spanning all terminals is constructed using greedy concatenation. New heuristics are compared with each other and with heuristics from the literature by performing extensive computational experiments on both randomly generated and library problem instances. Received October 27, 1997; revised May 7, 1998.     

A factoring approach for the Steiner tree problem in undirected networks

In communication networks, many applications, such as video on demand and video conferencing, must establish a communications tree that spans a subset K in a vertex set. The source node can then send identical data to all nodes in set K along this tree. This kind of communication is known as multicast communication. A network optimization problem, called the Steiner tree problem (STP), is presented to find a least cost multicasting tree. In this paper, an O(|E|) algorithm is presented to find a minimum Steiner tree for series-parallel graphs where |E| is the number of edges. Based on this algorithm, we proposed an O(2^2c·|E|) algorithm to solve the Steiner tree problem for general graphs where c is the number of applied factoring procedures. The c value is strongly related to the topology of a given graph. This is quite different from other algorithms with exponential time complexities in |K|.     

VPLS中具有时延约束机制的组播问题研究

VPLS作为一种革新的技术受到了广泛的关注和认可。但是，在用VPLS承载数据业务的时候还面临着一个复杂的难题：组播问题。传统的组播问题是具有NPC复杂度的Steiner问题。本文试图从应用和实现的角度出发，建立具有时延约束机制的组播转发机制。以建立最小时延树和最小开销树作为初始条件，运用循环迭代算法，求解满足时延约束的最小开销树。算法的复杂性为O（n^2）。作为补充，还提出了组播树的剪枝机制。试验结果表明，文中的算法简单可行，易于实现，适合应用于VPLS网络中。     

A practical algorithm for the minimum rectilinear steiner tree

An O(n^2) time approximation algorithm for the minimum rectilinear Steiner tree is proposed.The approximation ratio of the algorithm is strictly less than 1.5.The computing performances show the costs of the spanning trees produced by the algorithm are only 0.8% away from the optimal ones.