Pub Date : 2018-05-09DOI: 10.1201/9781420010749.ch43
I. Măndoiu, A. Kahng, A. Zelikovsky
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.
{"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}
Pub Date : 2018-05-09DOI: 10.1201/9781420010749.ch2
T. Gonzalez
{"title":"Basic Methodologies and Applications","authors":"T. Gonzalez","doi":"10.1201/9781420010749.ch2","DOIUrl":"https://doi.org/10.1201/9781420010749.ch2","url":null,"abstract":"","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":"130314193","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}
Pub Date : 2018-05-09DOI: 10.1201/9781351236423-38
M. Halldórsson, G. Kortsarz
This survey deals with problems at the intersection of two scientific fields: graph theory and scheduling. They can either be viewed as scheduling dependent jobs – jobs with resource conflicts – or as graph coloring optimization involving different objective functions. Our main aim is to illustrate the various interesting algorithmic techniques that have been brought to bear. We will also survey the state of the art, both in terms of approximation algorithms, lower bounds, and polynomial time solvability. We first formulate the problems, both from a scheduling and from a graph theory perspective, before setting the stage.
{"title":"Algorithms for Chromatic Sums, Multicoloring, and Scheduling Dependent Jobs","authors":"M. Halldórsson, G. Kortsarz","doi":"10.1201/9781351236423-38","DOIUrl":"https://doi.org/10.1201/9781351236423-38","url":null,"abstract":"This survey deals with problems at the intersection of two scientific fields: graph theory and scheduling. They can either be viewed as scheduling dependent jobs – jobs with resource conflicts – or as graph coloring optimization involving different objective functions. Our main aim is to illustrate the various interesting algorithmic techniques that have been brought to bear. We will also survey the state of the art, both in terms of approximation algorithms, lower bounds, and polynomial time solvability. We first formulate the problems, both from a scheduling and from a graph theory perspective, before setting the stage.","PeriodicalId":262519,"journal":{"name":"Handbook of Approximation Algorithms and Metaheuristics","volume":"529 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":"123356135","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}
{"title":"Rounding, Interval Partitioning and Separation","authors":"S. Sahni","doi":"10.1201/9781351236423-9","DOIUrl":"https://doi.org/10.1201/9781351236423-9","url":null,"abstract":"","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":"131220882","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}
Pub Date : 2018-05-09DOI: 10.1201/9781351236423-23
Marco Dorigo, Krzysztof Socha
Published as a chapter in Approximation Algorithms and Metaheuristics, a book edited by T. F. Gonzalez.
作为一章发表在近似算法和元启发式，一本由t.f.冈萨雷斯编辑的书。
{"title":"An Introduction to Ant Colony Optimization","authors":"Marco Dorigo, Krzysztof Socha","doi":"10.1201/9781351236423-23","DOIUrl":"https://doi.org/10.1201/9781351236423-23","url":null,"abstract":"Published as a chapter in Approximation Algorithms and Metaheuristics, a book edited by T. F. Gonzalez.","PeriodicalId":262519,"journal":{"name":"Handbook of Approximation Algorithms and Metaheuristics","volume":"29 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":"123541642","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}
Pub Date : 2018-05-09DOI: 10.1201/9781351236423-13
H. Hoos, T. Stützle
{"title":"Empirical Analysis of Randomised Algorithms","authors":"H. Hoos, T. Stützle","doi":"10.1201/9781351236423-13","DOIUrl":"https://doi.org/10.1201/9781351236423-13","url":null,"abstract":"","PeriodicalId":262519,"journal":{"name":"Handbook of Approximation Algorithms and Metaheuristics","volume":"15 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":"130121810","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}
Pub Date : 2018-05-09DOI: 10.1201/9781420010749.ch34
E. Coffman, J. Leung, J. Csirik
{"title":"Variable-Sized Bin Packing and Bin Covering","authors":"E. Coffman, J. Leung, J. Csirik","doi":"10.1201/9781420010749.ch34","DOIUrl":"https://doi.org/10.1201/9781420010749.ch34","url":null,"abstract":"","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":"129179121","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}
Pub Date : 2018-05-09DOI: 10.1201/9781420010749.ch5
G. Even
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.
{"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}
Pub Date : 2018-05-09DOI: 10.1201/9781420010749.ch30
B. Venkatachalam, David Fernández-Baca
{"title":"Sensitivity Analysis in Combinatorial Optimization","authors":"B. Venkatachalam, David Fernández-Baca","doi":"10.1201/9781420010749.ch30","DOIUrl":"https://doi.org/10.1201/9781420010749.ch30","url":null,"abstract":"","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":"125803415","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}
Pub Date : 2018-05-09DOI: 10.1201/9781420010749.ch12
P. Spirakis, S. Nikoletseas
{"title":"Randomized Approximation Techniques","authors":"P. Spirakis, S. Nikoletseas","doi":"10.1201/9781420010749.ch12","DOIUrl":"https://doi.org/10.1201/9781420010749.ch12","url":null,"abstract":"","PeriodicalId":262519,"journal":{"name":"Handbook of Approximation Algorithms and Metaheuristics","volume":"131 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":"121170204","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}
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