确定区域详细布线算法

提出了一种确定区域的详细布线算法,它能对不同设计模式进行布线。该算法能适用于任意多层布线情况,并且支持不同布线层具有的不同工艺参数,在构造布线树时,考虑芯片当前的走线拥挤度,使布线比较平均,并加快了算法运行速度、改善了布线质量,在连接两点线网时,构造基于二维迷宫布线结果的分层图,提出了一种对分层图的启发式染色算示来进行布线层分配,大大提高算法布线速度,采用拆线重布的方法来处理布线失败的线网。     

一种基于通孔数最小化的多层通道布线算法

该文提出了一种基于通孔数量小化的多层通道布线算法，算法采用非预留层模，首先根据线网之间的位置关系利用模拟退火算法将各线网合理地分配到对应的布线层中去，然后利用遗传算法得到相关布线层中线网的最佳布线顺序向量，最的根据得到的顺序向量利用“沉积法”将各线网布于合理的通道上，该算法克服了传统通孔优化算法中原始布线对优化结果的不利影响，使通孔的优化达到很好的效果。     

一种通孔最小化的三层通道布线算法

本文提出的连通孔最小化的三层通道布线算法,根据线网的接点位置建立线网分层图,并对此图进行三着色,确定出初始布线集和分拆线网集,通过引进线网次序图、压缩空段长度、填充原则和逐步排障法等,将初始布线集和拆网集的线网分配到相应的走线道上.实现线网的互连.本算法已用PASCAL语言编程,并在XT/286机上实现.结果表明,该算法不仅使通孔数大大减少,而且有些例子的走线道数也较一般布线法少.     

Priority-Based Routing Resource Assignment Considering Crosstalk

Crosstalk has become one of the most critical concerns in very deep sub-micron era. This paper deals with the problem of crosstalk mitigation at both methodological and algorithmic levels. Noting that intermediate operations between global routing and detailed routing are very effective in crosstalk estimation and reduction, the authors propose to incorporate several intermediate steps that are separated in traditional design flow into an integrated routing resource assignment stage, so that the operations could easily cooperate to fully exert their power on crosstalk reduction. An efficient priority-based heuristic algorithm is developed, which works slice by slice. Crosstalk avoidance, and many other aspects that are critical in routing practice including congestion, vias, layer preference, etc., are taken into account. A track reservation strategy is adopted in the algorithm framework to compensate the undesired effects caused by sequential routing. Experimental results on a series of ISPD98 and industrial benchmarks show that the proposed approach is able to reduce capacitive crosstalk by about 70% on average without compromising completion ratio compared with a previously reported graph based algorithm, demonstrating the advantages of the approach.     

High-performance MCM routing

The authors describe the multilayer MCM (multichip module) routing problem, and propose an approach for routing high-performance MCMs with the objective of minimizing interconnect delays and crosstalk. They first introduce an approach for rapidly estimating the time-domain response of lossy transmission line trees, and propose a realistic second-order delay model for MCM interconnects. The delay model is used to guide a performance-driven global routing algorithm. Given the 2-D global paths, the next stage is layer assignment. An effective algorithm for constrained layer assignment is developed. Based on the best-known maxcut approximation algorithm (which performs well in practice), a maximal k-color ordering is formulated for minimizing both interlayer and intralayer crosstalk as well as crossings in 3-D MCM substrates. The authors also propose a strategy that exhibits a good tradeoff between circuit performance and design cost, instead of concentrating exclusively on a single objective such as area minimization     

印制板布线的最佳路径快速通道分配算法

针对目前面向线网布线方法的某些不足,本文提出一种具有整体布线思想的最佳路径快速通道分配方法:对给定的线网按照一定的走线模式,根据代价函数,求出其最佳通道分配。它尤其适用于对连线长度有严格要求的超高速电路的布线问题。     

Diversified top-<Emphasis Type="Italic">k</Emphasis> clique search

Maximal clique enumeration is a fundamental problem in graph theory and has been extensively studied. However, maximal clique enumeration is time-consuming in large graphs and always returns enormous cliques with large overlaps. Motivated by this, in this paper, we study the diversified top-k clique search problem which is to find top-k cliques that can cover most number of nodes in the graph. Diversified top-k clique search can be widely used in a lot of applications including community search, motif discovery, and anomaly detection in large graphs. A naive solution for diversified top-k clique search is to keep all maximal cliques in memory and then find k of them that cover most nodes in the graph by using the approximate greedy max k-cover algorithm. However, such a solution is impractical when the graph is large. In this paper, instead of keeping all maximal cliques in memory, we devise an algorithm to maintain k candidates in the process of maximal clique enumeration. Our algorithm has limited memory footprint and can achieve a guaranteed approximation ratio. We also introduce a novel light-weight \(\mathsf {PNP}\)-\(\mathsf {Index}\), based on which we design an optimal maximal clique maintenance algorithm. We further explore three optimization strategies to avoid enumerating all maximal cliques and thus largely reduce the computational cost. Besides, for the massive input graph, we develop an I/O efficient algorithm to tackle the problem when the input graph cannot fit in main memory. We conduct extensive performance studies on real graphs and synthetic graphs. One of the real graphs contains 1.02 billion edges. The results demonstrate the high efficiency and effectiveness of our approach.     

一种改进的考虑噪声约束的过点分配方法

首先介绍了耦合电容计算、噪声模型选择以及串扰噪声的估计,接着详细分析了一种用于多层无网格区域布线的过点分配算法CPACNC（Crosspoint Assignment with Crosstalk Noise Control）。该算法首先根据障碍物信息将小方块边界分成多个区段,再分两步解CPA问题：CCPA（Coarse Crosspoint Assignment）和DCPA（Detailed Crosspoint Assignment）。针对CPACNC算法在进行边界分解时可能产生许多碎段的缺点,最后提出了一种修正算法,以处理边界分解时产生许多碎段的情况,使CPACNC方法更加有效。     

A parallel genetic algorithm for performance-driven VLSI routing

This paper presents a novel approach to solve the VLSI (very large scale integration) channel and switchbox routing problems. The approach is based on a parallel genetic algorithm (PGA) that runs on a distributed network of workstations. The algorithm optimizes both physical constraints (length of nets, number of vias) and crosstalk (delay due to coupled capacitance). The parallel approach is shown to consistently perform better than a sequential genetic algorithm when applied to these routing problems. An extensive investigation of the parameters of the algorithm yields routing results that are qualitatively better or as good as the best published results. In addition, the algorithm is able to significantly reduce the occurrence of crosstalk     

一种借助邻接矩阵求任意图最大团的方法

最大团问题是图论中重要的NPC问题。文章以一种新的方法,通过矩阵运算选择图上可能存在最大团的分支,进而实现求解最大团的问题。算法的每一个步骤都可以用成熟的并行方法替代。     

基于局部有限搜索的无向图近似最大团快速求解算法

无向图最大团求解是一个著名的NP-完全问题,解决该问题的经典算法基本上都采用完全精确搜索策略。鉴于NP-完全问题本身所固有的复杂性,这些算法或许仅适用于某些特殊的小规模图,对于具有大规模顶点和边的复杂图还是显得无力,难以适用。针对完全精确搜索策略下的无向图最大团求解算法的大部分时间都用于对图进行额外而无效的查找的问题,采用分划递归技术将图划分为邻接子图和悬挂子图,然后对邻接子图进行递归求解,而对悬挂子图则通过设置搜索范围控制函数进行局部有限搜索。在DIMACS数据集上将所提算法与当前主要的最大团求解算法进行对比实验,结果表明,文中提出的局部有限搜索求解策略能在75%的基准数据上获得最大团,剩下不能得到最大团的数据实际上也可以获得接近于最大团的近似最大团,但算法的平均求解时间仅为目前最大团精确求解算法的20%左右。因此,在很多最大团非精确要求的场景中,所提算法具有极高的应用价值。     

求解图的最大团的一种算法

图的最大团问题是一个著名的ＮＰ－完全问题．现有求解图的最大团的算法或者只适用于某些特殊的图,或者需要指数级时间代价,效率较低．以图的区间表示的概念为基础,提出了一种求解最大团的算法．该算法能够适用于任意的简单图,并且在一定的条件下,该算法只需要多项式时间就可以完成运行.     

基于最大权团的曲面粗匹配算法

提出一种将曲面匹配问题转化为图论中的最大权团搜索问题、将最优的点对应关系用最大权团表示的曲面粗匹配算法,该算法分为点匹配、点对应图构造和最大权团生成等3个阶段.点匹配使用高曲率点和均匀采样点作为候选点,通过自旋图进行匹配计算,构造初始点对应集合;点对应图构造使用距离约束、法矢约束和唯一性约束构造图的边,并使用自旋图相关系数为顶点赋权值;最大权团生成使用基于分支限界的团搜索算法,从对应点图中提取出代表最优对应的最大权团.实验结果表明,文中算法稳定、有效、可扩展,能够进行部分曲面匹配,并且适用于欠特征曲面.     

基于混合离散粒子群优化的轨道分配算法

现有的轨道分配工作大多忽略局部线网问题,并且容易陷入局部极值.为此,文中基于离散粒子群优化、遗传操作和基于协商的精炼策略,综合考虑局部线网、重叠冲突、线长和障碍物,提出轨道分配算法.算法抽象局部线网,构建对应的线段模型.为了扩大种群多样性,混合遗传操作以提高全局搜索效率.同时,设计简单高效的适应度函数.最后,使用基于协商的精炼策略进一步减少线段重叠.实验表明文中算法的有效性,该算法可以获得较佳的重叠代价指标优化值,减少关键布线区域的拥挤情况.     

一种新的与线网顺序无关的随机优化总体布线算法

针对目前总体布线中仍然存在的3个关键问题;布线结果受布线顺序的影响、总体布线图中拥挤区域的不可预见性、线网连接式样受到算法的限制等,该文提出了一种新的不受线网顺序影响的总体布线算法,并实现了相应的总体布线器RINO－Router。该算法采用随机优化方法来保 证先后被拆线重布的线网有相同的通过拥挤区域的机会,并能得到GRG边的拥挤度估计值;采用高效的Steiner树改造算法构造避开拥挤区域的布线树,采用典型电路实例进行了测试,并将布线结果与基于多商品流算法的总体布线器Matula-Router进行了对比。结果表明,RINO－Router能够在短得多的运行时间内求得质量与Matula-Router相近的总体布线解。     

Hexagonal Models for Channel Routing

In this paper we present new diagonal routing models based on the hexagonal grid, and investigate the potential of these models in terms of channel routing. The hexagonal grid consists of vertical columns, and positive and negative diagonal tracks with slopes and , respectively. The layout geometry of this grid is examined and shown to be compatible with VLSI implementation. Furthermore, this investigation demonstrates some advantages of routing on the hexagonal grid. For a channel routing problem (CRP) having maximum net span s ^* , we give an algorithm which routes any two-sided (two-terminal or multiterminal) net CRP in width in three reserved layers. For densities , this channel width is less than the lower bound of d for routing on the square grid in three nonreserved layers. For CRPs of large span, we show how a previous square grid algorithm can be adapted to the hexagonal grid to obtain three layer routings of width for two-terminal nets and for multiterminal nets. Received November 4, 1994; revised August 7, 1995.     

2-local 5/4-competitive algorithm for multicoloring triangle-free hexagonal graphs

An important optimization problem in the design of cellular networks is to assign sets of frequencies to transmitters to avoid unacceptable interference. A cellular network is generally modeled as a subgraph of the infinite triangular lattice. The distributed frequency assignment problem can be abstracted as a multicoloring problem on a weighted hexagonal graph, where the weight vector represents the number of calls to be assigned at vertices. In this paper we present a 2-local distributed algorithm for multicoloring triangle-free hexagonal graphs using only the local clique numbers ω₁(v) and ω₂(v) at each vertex v of the given hexagonal graph, which can be computed from local information available at the vertex. We prove that the algorithm uses no more than colors for any triangle-free hexagonal graph G, without explicitly computing the global clique number ω(G). Hence the competitive ratio of the algorithm is 5/4.     

最大团问题的改进蚁群算法求解

为了更好的解决最大团问题,提出一种改进的蚁群算法。通过提取图的顶点信息,将图用信息素模型来表示;根据最大团问题的约束条件利用蚁群构造极大团,并进行实时的全局信息素更新和局部信息素更新,直到找到最大团。实验结果表明,算法能较好的实现最大团问题,算法性能高于通用的蚁群算法。     

消除拥挤的多层总体布线新流程

提出一种在布线前进行层分配的总体布线算法,基于一个多层布线的新流程,使用包含线网所有端点的边界盒来估计线网拥挤度,并基于拥挤度均匀的目标把线网分配到不同层对上.该算法已经实现并进行了测试,实验结果证明了其有效性.     

A multipopulation parallel genetic simulated annealing-based QoS routing and wavelength assignment integration algorithm for multicast in optical networks

In this paper, we propose an integrated Quality of Service (QoS) routing algorithm for optical networks. Given a QoS multicast request and the delay interval specified by users, the proposed algorithm can find a flexible-QoS-based cost suboptimal routing tree. The algorithm first constructs the multicast tree based on the multipopulation parallel genetic simulated annealing algorithm, and then assigns wavelengths to the tree based on the wavelength graph. In the algorithm, routing and wavelength assignment are integrated into a single process. For routing, the objective is to find a cost suboptimal multicast tree. For wavelength assignment, the objective is to minimize the delay of the multicast tree, which is achieved by minimizing the number of wavelength conversion. Thus both the cost of multicast tree and the user QoS satisfaction degree can approach the optimal. Our algorithm also considers load balance. Simulation results show that the proposed algorithm is feasible and effective. We also discuss the practical realization mechanisms of the algorithm.