求解VLSI布线问题的离散粒子群优化算法

最小矩形Stcincr树问题是VI_SI布线的一个关键问题,且是一个典型的NP完全问题。为了有效地解决VLSI布线中考虑障碍物的最小矩形St einer树问题,提出了一种改进的离散粒子群优化算法。考虑到存在障碍物,设计了一个基于惩罚的适应度函数。引入了遗传算法的变异和交又算子,增加了种群的多样性并适当地扩展了粒子的寻优范围。实验结果表明,算法是有效的,实现简单,且相对遗传算法能更有效迅速地收敛。     

Fast heuristic algorithms for rectilinear steiner trees

A fundamental problem in circuit design is how to connectn points in the plane, to make them electrically common using the least amount of wire. The tree formed, a Steiner tree, is usually constructed with respect to the rectilinear metric. The problem is known to be NP-complete; an extensive review of proposed heuristics is given. An early algorithm by Hanan is shown to have anO(n logn) time implementation using computational geometry techniques. The algorithm can be modified to do sequential searching inO(n ²) total time. However, it is shown that the latter approach runs inO(n ^3/2) expected time, forn points selected from anm×m grid. Empirical results are presented for problems up to 10,000 points.     

Fast heuristic algorithms for rectilinear steiner trees

A fundamental problem in circuit design is how to connectn points in the plane, to make them electrically common using the least amount of wire. The tree formed, a Steiner tree, is usually constructed with respect to the rectilinear metric. The problem is known to be NP-complete; an extensive review of proposed heuristics is given. An early algorithm by Hanan is shown to have anO(n logn) time implementation using computational geometry techniques. The algorithm can be modified to do sequential searching inO(n ²) total time. However, it is shown that the latter approach runs inO(n ^3/2) expected time, forn points selected from anm×m grid. Empirical results are presented for problems up to 10,000 points.     

求解绝对值距离Steiner最小树的改进元胞蚂蚁算法

绝对值距离Steiner最小树问题是在集成电路布线等领域应用广泛的属于NP难的经典组合优化问题,由于该问题的搜索空间与元胞自动机的结构相似,设计了求解绝对值距离Steiner最小树问题的改进的元胞蚂蚁算法。经大量数据实验表明,该算法要比最小生成树平均改进15%,优于多数已有的基于最小生成树的近似算法,验证了算法的实用性。     

基于非hanan点的时延约束最小斯坦那树生成方法

介绍了一个基于非hanan点的时延约束最小斯坦那树生成方法,该方法引入非hanan点的概念,可以得到长度费用优化较好的布线树.     

Internet高性能组播路由算法研究

为了进一步适应Internet网络多媒体业务应用,高性能Internet组播路由算法已成为国内外网络研究熟点和难点问题之一。分析了组播路由问题的定义和分类;论述了现有的IP层组播路由算法,主要包括五种类型：最多路径树算法、最小生成树算法、Steiner树算法、单约束的Steiner树算法和多约束的Steiner树算法;并对它们进行比较和评价。最后提出了高性能Internet组播路由算法具有的特点和进一步的研究方向。     

近乎最佳的Manhattan型Steiner树近似算法

求解最佳的Manhattan型Steiner树问题(minimum rectilinear Steiner tree,简记为MRST问题)是在VLSI布线、网络通信中所遇到的组合优化问题,同时也是一个NP-难解问题.该文给出对该问题的O(n²)时间复杂性的近似算法.该算法在最坏情况下的近似比严格小于3/2.计算机实验结果表明,所求得的支撑树的平均费用与最佳算法的平均费用仅相差0.8%.该算法稍加修改,可应用到三维或多维的Manhattan空间对Steiner问题求解,且易于在并行与分布式环境下编程实现     

The class Steiner minimal tree problem: a lower bound and test problem generation

The class Steiner minimal tree problem is an extension of the standard Steiner minimal tree problem in graphs, motivated by the problem of wire routing in the area of physical design of very large scale integration (VLSI). This problem is NP-hard, even if there are no Steiner nodes and the graph is a tree; moreover, there exists no polynomial time approximation algorithm with a constant bound on the relative error under the hypothesis that P NP [16]. Hence, fast and good heuristic algorithms are needed in practice. In this paper, we present an integer programming formulation of the problem. Using Lagrangean relaxation and subgradient optimization, we derive a lower bound. In order to test the lower bound, we present a procedure for generating test problems for the class Steiner minimal tree problem that have known optimal solutions. The computational experiments for the test problems demonstrate that the lower bound is very tight and differs from the optimal solutions by only a few percent on average for sparse graphs. Received: 5 July 1999 / Revised version: 14 July 2000     

Two probabilistic results on rectilinear steiner trees

In recent years, researchers have proven many theorems of the following form: given points distributed according to a Poisson process with intensity parameterN on the unit square, the length of the shortest spanning tree (rectilinear Steiner tree, traveling salesman tour, or some other functional) on these points is, with probability one, asymptotic to β√N for some constant β (which is presumably different for different functionals). Though these theorems are well understood, very little is known about the constants β. In this paper we prove that the constants in the cases of rectilinear spanning tree and rectilinear Steiner tree do, indeed, differ. This proof is constructive in the sense that we give a polynomial-time heuristic algorithm that produces a Steiner tree of expected length some fraction shorter than a minimum spanning tree. We continue the analysis to prove a second result: the expected value of the minimum number of Steiner points in a shortest rectilinear Steiner tree grows linearly withN.     

基于共享边的时延约束组播路由算法

为了优化在时延约束下的组播树代价,降低算法计算复杂度,研究了时延受限的Steiner树问题.分析了最短路径启发式(MPH)算法的执行过程,以此为基础提出一个基于共享边的时延约束组播路由算法ESAMPH.该算法在构建组播路由树时能够优先采用包含有较多的最短路径经过的节点,这样后面的组播成员节点到树上的最短路径也有可能经过这些节点,由此实现边的共享,降低了组播树的代价.仿真结果表明,ESAMPH算法在代价、延迟和计算时间之间能获得较好的平衡,综合性能较好.     

欧氏Steiner最优树的快速算法

针对欧氏平面内连接固定原点的最小树长问题,即欧氏Steiner最优树问题,给出了插入算法、递增优化算法、遗传算法等三种快速算法,并在微机上予以实现。经大量实例测试和结果比较,获得了满意的效果。     

基于量子遗传算法的QoS多播路由算法

QoS多播路由算法的核心问题就是建立满足QoS约束的多播树,它是计算机网络中著名的受约束最小Steiner树问题,是一个NP完全问题。量子遗传算法是基于量子计算理论的新型遗传算法,基于量子遗传算法的基本原理,提出了QoS约束的多播路由算法（QoSMR-QGA）,并详细介绍了QoSMR-QGA算法的实现过程。仿真实验表明,该算法具有较好的算法收敛性和多播路由成功率。     

一种含浮动端点的斯坦纳树的构造算法

在集成电路的自动布图技术中，在完成布局过程，即各模块（或子电路单元）的拓扑位置确定以后，布线需要完成各电路模块之间的连接。斯坦纳树的构造问题可以应用于总体布线；如果考虑已有单元或连线的障碍，它也可以应用于详细布线。     

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).     

基于遗传算法的带宽-时延约束多播路由优化算法

随着许多多媒体在高速网络中的应用,多播路由问题成为越来越重要的课题。多播路由问题在计算机网络中是著名的Steiner树问题,同时也是NP完全问题。该文提出了一种基于遗传算法的多播路由优化算法,采用可变长度染色体(多播树)和基因(路径)应用于编码问题。该算法在满足带宽和时延约束条件下寻找代价最小的多播树。仿真实验证明该算法能快速找到最优解,收敛速度快,可靠性高,能够满足多媒体网络对实时性的要求。     

A note on distributed multicast routing in point-to-point networks

The distributed algorithm for a multicast connection set-up, based on the ‘cheapest insertion’ heuristic, is reviewed. The multicast routing problem is translated into a Steiner tree problem in point-to-point networks where nodes have only a limited knowledge about the network. A solution is proposed in which the time complexity and the amount of information exchanged between network nodes are proportional to the number of members of the multicast group. The Steiner tree is constructed by means of a distributed table-passing algorithm. The analysis of the algorithm presented, backed up by simulation results, confirms its superiority over the algorithm based on ‘waving technique’.Scope and purposeMulticasting is a mechanism used in communication networks that allows distribution of information from a single source to multiple destinations. The problem of finding a multicast connection for a static group of communicating entities in connection-oriented point-to-point network can be formulated in graph theory as a minimum Steiner tree problem. Due to NP-completeness of the Steiner tree problem multicast, routing algorithms are based on heuristics. The diversity of network environments and the lack of centralised information about network topology require an effective distribution of the multicast routing algorithms among the network nodes. This article presents an alternative to the distributed algorithm proposed by Rugelj and Klavzar that implements the same heuristics for the construction of a minimum cost multicast connection in point-to-point networks. The present algorithm constitutes a substantial improvement over that previously proposed with regard to running time and the amount of the information exchanged between network nodes.     

基于自适应PSO和混合转换策略的X结构Steiner最小树算法

X结构Steiner最小树(XSMT)是非曼哈顿结构总体布线算法中多端线网的最佳连接模型,属于NP难问题.文中基于混合转换策略和自适应粒子群优化算法,提出XSMT构造算法.首先设计有效的混合转换策略,扩大算法寻优空间,提高算法收敛效率.为了满足粒子编码的健全性,算法的更新方式引入带并查集策略的交叉和变异算子,同时采取自适应调整学习因子的策略,加快粒子群优化算法的收敛速度.实验表明,文中算法能得到较好的XSMT求解方案,获得多种不同拓扑的XSMTs,有利于VLSI总体布线阶段的拥挤度优化.     

并行量子遗传算法在QoS组播路由中的应用

随着网络通信技术的发展和Internet的普及,性能出色的组播路由越来越重要。著名的组播路由Steiner树问题是NP完全问题,应采用启发式方法求解。文中在常规量子遗传算法中引入并行进化模型,提出了一种解决多约束QoS组播路由优化问题的算法。在满足带宽、时延约束条件下寻找代价最小的组播树,并合理安排节点负荷,减少通信开销。仿真实验结果表明本算法搜索速度快、全局寻优能力强,性能和效率优于常规量子遗传算法。     

基于MPH的时延约束Steiner树算法

为了在时延约束条件下进一步优化组播树代价,并降低算法计算复杂度,研究了时延受限的Steiner树问题.分析了MPH(minimum path heuristic)算法的计算复杂度;在此基础上设计了一个时延约束Steiner树算法DCMPH(delay constrained MPH)用于构造时延约束最小代价组播树.该算法中每个目的结点通过与当前组播树有最小代价的路径加入组播树;若时延不满足要求,则通过合并最小时延SPT(shortest path tree)树进而产生一个满足时延约束的最小代价组播树.仿真实验表明,DCMPH算法生成的组播树在保证时延要求的情况下,与同类算法相比取得了很好的代价性能和较低的计算复杂度.     

Algorithms for multicast connection under multi-path routing model

Given a source node and a set of destination nodes in a network, multicast routing problem is usually treated as Steiner tree problem. Unlike this well-known tree based routing model, multicast routing under multi-path model is to find a set of paths rooted at the source node such that in each path at most a fixed number of destination nodes can be designated to receive the data and every destination node must be designated in a path to receive the data. The cost of routing is the total costs of paths found. In this paper we study how to construct a multicast routing of minimal cost under multi-path model. We propose two approximation algorithms for this NP-complete problem with guaranteed performance ratios.