Handbook of Approximation Algorithms and Metaheuristics最新文献_第2页

Practical Approximations of Steiner Trees in Uniform Orientation Metrics 斯坦纳树在均匀方向度量中的实用逼近

Handbook of Approximation Algorithms and Metaheuristics Pub Date : 2018-05-09 DOI: 10.1201/9781420010749.ch43

I. Măndoiu, A. Kahng, A. Zelikovsky

{"title":"Practical Approximations of Steiner Trees in Uniform Orientation Metrics","authors":"I. Măndoiu, A. Kahng, A. Zelikovsky","doi":"10.1201/9781420010749.ch43","DOIUrl":"https://doi.org/10.1201/9781420010749.ch43","url":null,"abstract":"The Steiner minimum tree problem, which asks for a minimum-length interconnection of a given set of terminals in the plane, is one of the fundamental problems in Very Large Scale Integration (VLSI) physical design. Although advances in VLSI manufacturing technologies have introduced additional routing objectives, minimum length continues to be the primary objective when routing non-critical nets, since the minimum-length interconnection has minimum total capacitance and occupies minimum amount of area. To simplify design and manufacturing, VLSI interconnect is restricted to a small number of orientations defining the so called interconnect architecture. Until recently, designers have relied almost exclusively on the Manhattan interconnect architecture, which allows interconnect routing along two orthogonal directions. However, non-Manhattan interconnect architectures – such as the Y-architecture, which allows 0, 120, and 240 oriented wires, and the X-architecture, which allows 45 diagonal wires in addition to the traditional horizontal and vertical orientations – are becoming increasingly attractive due to the significant potential for reducing interconnect length (see, e.g., [4, 5, 16, 22, 24, 25, 27]). A common generalization of interconnect architectures of interest in VLSI design is that of uniform orientation metric, or λ-geometry, in which routing is allowed only along λ ≥ 2 orientations forming consecutive angles of π/λ. The Manhattan, Y-, and X-architectures correspond to λ = 2, 3, and 4, respectively.","PeriodicalId":262519,"journal":{"name":"Handbook of Approximation Algorithms and Metaheuristics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124352921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Basic Methodologies and Applications 基本方法及应用

Handbook of Approximation Algorithms and Metaheuristics Pub Date : 2018-05-09 DOI: 10.1201/9781420010749.ch2

T. Gonzalez

引用次数: 0

Algorithms for Chromatic Sums, Multicoloring, and Scheduling Dependent Jobs 色和、多色和调度相关作业的算法

Handbook of Approximation Algorithms and Metaheuristics Pub Date : 2018-05-09 DOI: 10.1201/9781351236423-38

M. Halldórsson, G. Kortsarz

引用次数: 0

Rounding, Interval Partitioning and Separation 四舍五入，区间划分和分离

Handbook of Approximation Algorithms and Metaheuristics Pub Date : 2018-05-09 DOI: 10.1201/9781351236423-9

S. Sahni

引用次数: 0

An Introduction to Ant Colony Optimization 蚁群优化导论

Handbook of Approximation Algorithms and Metaheuristics Pub Date : 2018-05-09 DOI: 10.1201/9781351236423-23

Marco Dorigo, Krzysztof Socha

引用次数: 78

Empirical Analysis of Randomised Algorithms 随机算法的实证分析

Handbook of Approximation Algorithms and Metaheuristics Pub Date : 2018-05-09 DOI: 10.1201/9781351236423-13

H. Hoos, T. Stützle

引用次数: 0

Variable-Sized Bin Packing and Bin Covering 可变尺寸的桶包装和桶盖

Handbook of Approximation Algorithms and Metaheuristics Pub Date : 2018-05-09 DOI: 10.1201/9781420010749.ch34

E. Coffman, J. Leung, J. Csirik

引用次数: 18

Recursive Greedy Methods 递归贪心方法

Handbook of Approximation Algorithms and Metaheuristics Pub Date : 2018-05-09 DOI: 10.1201/9781420010749.ch5

G. Even

{"title":"Recursive Greedy Methods","authors":"G. Even","doi":"10.1201/9781420010749.ch5","DOIUrl":"https://doi.org/10.1201/9781420010749.ch5","url":null,"abstract":"Greedy algorithms are often the first algorithm that one considers for various optimization problems, and ,in particular, covering problems. The idea is very simple: try to build a solution incrementally by augmenting a partial solution. In each iteration, select the “best” augmentation according to a simple criterion. The term greedy is used because the most common criterion is to select an augmentation that minimizes the ratio of “cost” to “advantage”. We refer to the cost-to-advantage ratio of an augmentation as the density of the augmentation. In the Set-Cover (SC) problem, every set S has a weight (or cost) w(S). The “advantage” of a set S with respect to a partial cover {S1, . . . , Sk} is the number of new elements covered by S, i.e., |S (S1 ∪ . . .∪Sk)|. In each iteration, a set with a minimum density is selected and added to the partial solution until all the elements are covered. In the SC problem, it is easy to find an augmentation with minimum density simply by re-computing the density of every set in every iteration. In this chapter we consider problems for which it is NP-hard to find an augmentation with minimum ∗Chapter 3 from: Handbook of Approximation Algorithms and Metaheuristics edited by Teofilo Gonzalez.","PeriodicalId":262519,"journal":{"name":"Handbook of Approximation Algorithms and Metaheuristics","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131982185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 7

Sensitivity Analysis in Combinatorial Optimization 组合优化中的灵敏度分析

Handbook of Approximation Algorithms and Metaheuristics Pub Date : 2018-05-09 DOI: 10.1201/9781420010749.ch30

B. Venkatachalam, David Fernández-Baca

引用次数: 47

Randomized Approximation Techniques 随机逼近技术

Handbook of Approximation Algorithms and Metaheuristics Pub Date : 2018-05-09 DOI: 10.1201/9781420010749.ch12

P. Spirakis, S. Nikoletseas

引用次数: 0