Obstacle-avoiding rectilinear Steiner tree.

Li, Liang.Thesis (M.Phil.)--Chinese University of Hong Kong, 2009.Includes bibliographical references (leaves 57-61).Abstract also in Chinese.Abstract --- p.iAcknowledgement --- p.ivChapter 1 --- Introduction --- p.1Chapter 1.1 --- Background --- p.1Chapter 1.1.1 --- Partitioning --- p.1Chapter 1.1.2 --- Floorplanning and Placement --- p.2Chapter 1.1.3 --- Routing --- p.2Chapter 1.1.4 --- Compaction --- p.3Chapter 1.2 --- Motivations --- p.3Chapter 1.3 --- Problem Formulation --- p.4Chapter 1.3.1 --- Properties of OARSMT --- p.4Chapter 1.4 --- Progress on the Problem --- p.4Chapter 1.5 --- Contributions --- p.5Chapter 1.6 --- Thesis Organization --- p.6Chapter 2 --- Literature Review on OARSMT --- p.8Chapter 2.1 --- Introduction --- p.8Chapter 2.2 --- Previous Methods --- p.9Chapter 2.2.1 --- OARSMT --- p.9Chapter 2.2.2 --- Shortest Path Problem with Blockages --- p.13Chapter 2.2.3 --- OARSMT with Delay Minimization --- p.14Chapter 2.2.4 --- OARSMT with Worst Negative Slack Maximization --- p.14Chapter 2.3 --- Comparison --- p.15Chapter 3 --- Heuristic Method --- p.17Chapter 3.1 --- Introduction --- p.17Chapter 3.2 --- Our Approach --- p.18Chapter 3.2.1 --- Handling of Multi-pin Nets --- p.18Chapter 3.2.2 --- Propagation --- p.20Chapter 3.2.3 --- Backtrack --- p.23Chapter 3.2.4 --- Finding MST --- p.26Chapter 3.2.5 --- Local Refinement Scheme --- p.26Chapter 3.3 --- Experimental Results --- p.28Chapter 3.4 --- Summary --- p.28Chapter 4 --- Exact Method --- p.32Chapter 4.1 --- Introduction --- p.32Chapter 4.2 --- Review on GeoSteiner --- p.33Chapter 4.3 --- Overview of our Approach --- p.33Chapter 4.4 --- FST with Virtual Pins --- p.34Chapter 4.4.1 --- Definition of FST --- p.34Chapter 4.4.2 --- Notations --- p.36Chapter 4.4.3 --- Properties of FST with Virtual Pins --- p.36Chapter 4.5 --- Generation of FST with Virtual Pins --- p.46Chapter 4.5.1 --- Generation of FST with Two Pins --- p.46Chapter 4.5.2 --- Generation of FST with 3 or More Pins --- p.48Chapter 4.6 --- Concatenation of FSTs with Virtual Pins --- p.50Chapter 4.7 --- Experimental Results --- p.52Chapter 4.8 --- Summary --- p.53Chapter 5 --- Conclusion --- p.55Bibliography --- p.6

On the construction of rectilinear Steiner minimum trees among obstacles.

Rectilinear Steiner minimum tree (RSMT) problem asks for a shortest tree spanning a set of given terminals using only horizontal and vertical lines. Construction of RSMTs is an important problem in VLSI physical design. It is useful for both the detailed and global routing steps, and it is important for congestion, wire length and timing estimations during the floorplanning or placement step. The original RSMT problem assumes no obstacle in the routing region. However, in today’s designs, there can be many routing blockages, like macro cells, IP blocks and pre-routed nets. Therefore, the RSMT problem with blockages has become an important problem in practice and has received a lot of research attentions in the recent years. The RSMT problem has been shown to be NP-complete, and the introduction of obstacles has made this problem even more complicated.In the first part of this thesis, we propose an exact algorithm, called ObSteiner, for the construction of obstacle-avoiding RSMT (OARSMT) in the presence of complex rectilinear obstacles. Our work is developed based on the GeoSteiner approach in which full Steiner trees (FSTs) are first constructed and then combined into a RSMT. We modify and extend the algorithm to allow rectilinear obstacles in the routing region. We prove that by adding virtual terminals to each routing obstacle, the FSTs in the presence of obstacles will follow some very simple structures. A two-phase approach is then developed for the construction of OARSMTs. In the first phase, we generate a set of FSTs. In the second phase, the FSTs generated in the first phase are used to construct an OARSMT. Experimental results show that ObSteiner is able to handle problems with hundreds of terminals in the presence of up to two thousand obstacles, generating an optimal solution in a reasonable amount of time.In the second part of this thesis, we propose the OARSMT problem with slew constraints over obstacles. In modern VLSI designs, obstacles usually block a fraction of metal layers only making it possible to route over the obstacles. However, since buffers cannot be place on top of any obstacle, we should avoid routing long wires over obstacles. Therefore, we impose the slew constraints for the interconnects that are routed over obstacles. To deal with this problem, we analyze the optimal solutions and prove that the internal trees with signal direction over an obstacle will follow some simple structures. Based on this observation, we propose an exact algorithm, called ObSteiner with slew constraints, that is able to find an optimal solution in the extended Hanan grid. Experimental results show that the proposed algorithm is able to reduce nearly 5% routing resources on average in comparison with the OARSMT algorithm and is also very much faster.Huang, Tao.Thesis (Ph.D.)--Chinese University of Hong Kong, 2013.Includes bibliographical references (leaves [137]-144).Chapter 1 --- Introduction --- p.1Chapter 1.1 --- The rectilinear Steiner minimum tree problem --- p.1Chapter 1.2 --- Applications --- p.3Chapter 1.3 --- Obstacle consideration --- p.5Chapter 1.4 --- Thesis outline --- p.6Chapter 1.5 --- Thesis contributions --- p.8Chapter 2 --- Background --- p.11Chapter 2.1 --- RSMT algorithms --- p.11Chapter 2.1.1 --- Heuristics --- p.11Chapter 2.1.2 --- Exact algorithms --- p.20Chapter 2.2 --- OARSMT algorithms --- p.30Chapter 2.2.1 --- Heuristics --- p.30Chapter 2.2.2 --- Exact algorithms --- p.33Chapter 3 --- ObSteiner - an exact OARSMT algorithm --- p.37Chapter 3.1 --- Introduction --- p.38Chapter 3.2 --- Preliminaries --- p.39Chapter 3.2.1 --- OARSMT problem formulation --- p.39Chapter 3.2.2 --- An exact RSMT algorithm --- p.40Chapter 3.3 --- OARSMT decomposition --- p.42Chapter 3.3.1 --- Full Steiner trees among complex obstacles --- p.42Chapter 3.3.2 --- More Theoretical results --- p.59Chapter 3.4 --- OARSMT construction --- p.62Chapter 3.4.1 --- FST generation --- p.62Chapter 3.4.2 --- Pruning of FSTs --- p.66Chapter 3.4.3 --- FST concatenation --- p.71Chapter 3.5 --- Incremental construction --- p.82Chapter 3.6 --- Experiments --- p.83Chapter 4 --- ObSteiner with slew constraints --- p.97Chapter 4.1 --- Introduction --- p.97Chapter 4.2 --- Problem Formulation --- p.100Chapter 4.3 --- Overview of our approach --- p.103Chapter 4.4 --- Internal tree structures in an optimal solution --- p.103Chapter 4.5 --- Algorithm --- p.126Chapter 4.5.1 --- EFST and SCIFST generation --- p.127Chapter 4.5.2 --- Concatenation --- p.129Chapter 4.5.3 --- Incremental construction --- p.131Chapter 4.6 --- Experiments --- p.131Chapter 5 --- Conclusion --- p.135Bibliography --- p.13

Geometric-based Optimization Algorithms for Cable Routing and Branching in Cluttered Environments

The need for designing lighter and more compact systems often leaves limited space for planning routes for the connectors that enable interactions among the system’s components. Finding optimal routes for these connectors in a densely populated environment left behind at the detail design stage has been a challenging problem for decades. A variety of deterministic as well as heuristic methods has been developed to address different instances of this problem. While the focus of the deterministic methods is primarily on the optimality of the final solution, the heuristics offer acceptable solutions, especially for such problems, in a reasonable amount of time without guaranteeing to find optimal solutions. This study is an attempt to furthering the efforts in deterministic optimization methods to tackle the routing problem in two and three dimensions by focusing on the optimality of final solutions. The objective of this research is twofold. First, a mathematical framework is proposed for the optimization of the layout of wiring connectors in planar cluttered environments. The problem looks at finding the optimal tree network that spans multiple components to be connected with the aim of minimizing the overall length of the connectors while maximizing their common length (for maintainability and traceability of connectors). The optimization problem is formulated as a bi-objective problem and two solution methods are proposed: (1) to solve for the optimal locations of a known number of breakouts (where the connectors branch out) using mixed-binary optimization and visibility notion and (2) to find the minimum length tree that spans multiple components of the system and generates the optimal layout using the previously-developed convex hull based routing. The computational performance of these methods in solving a variety of problems is further evaluated. Second, the problem of finding the shortest route connecting two given nodes in a 3D cluttered environment is considered and addressed through deterministically generating a graphical representation of the collision-free space and searching for the shortest path on the found graph. The method is tested on sample workspaces with scattered convex polyhedra and its computational performance is evaluated. The work demonstrates the NP-hardness aspect of the problem which becomes quickly intractable as added components or increase in facets are considered

Single-Family Residential Development in DeKalb County 1945-1970

The Case studies class of spring of 2010 compiled this resource material. This study focused on suburban residential developments in DeKalb County, Georgia between the end of World War II and 1970 in order to better understand the transformation of the area after the Second World War. The resource includes data on national residential trends, architectural and landscape designs, as well as information on metropolitan Atlanta. The resource was created to support the effort to preserve local neighborhoods, buildings, and landmarks by providing the historic context in which they were created.https://scholarworks.gsu.edu/history_heritagepreservation/1038/thumbnail.jp

An evaluation of small scale shortwave vegetation index imagery for vegetation mapping.

Incl. 1 article reprintSIGLEAvailable from British Library Document Supply Centre- DSC:DX85252 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Removal Period Cherokee Households in Southwestern North Carolina: Material Perspectives on Ethnicity and Cultural Differentiation

Nineteenth century accounts of Cherokee Indian society consistently refer to the existence of two classes among the Cherokees: the acculturated mixed blood[s], who speak English and are considered the intelligent and wealthy class and the culturally conservative fullbloods, whom white observers denigrated as backward, indolent, and ignorant pagans. This perceived dichotomy reflected the poles of a socioeconomic and cultural continuum that developed as a result of the differential Westernization of Cherokee individuals and households during the post-Revolutionary War era. As these socioeconomic classes diverged, they developed as the primary axis of competition and conflict within Cherokee society. Because these groups were progressively distinguished by ancestry, language use, lifestyle, and ideology, they may be characterized as emergent ethnic groups subsumed within the Cherokee national polity. As identity-conscious groups in competition for economic resources and political power, the Cherokee-speaking fullblood majority and the English-speaking metis minority used various media, including material goods and property, to construct and maintain ethnic boundaries. This study examines documentary and archaeological evidence for the use of such material media by Cherokee families in southwestern North Carolina during the Removal period. (1835-1838) and seeks to define material patterning that distinguished the English-speaking metis minority from the Cherokee-speaking fullblood majority. Four independent primary datasets are successively analyzed and discussed to accomplish a synthetic overview of Cherokee wealthholding and material culture. Bioracial, linguistic, and certain aspects of economic variation within the study population are defined through examination of the 1835 War Department census of the Cherokee Nation east of the Mississippi. General trends of bioracial endogamy, community composition, and wealth distribution evident in the 1835 census indicate active ethnic differentiation within the Cherokee population of southwestern North Carolina. The population of the study area was ethnically and socioeconomically homogeneous, with a dominant component of monolingual Cherokee fullblood subsistence farmers who formed a distinctly conservative and materially impoverished aboriginal stratum of Cherokee society. Contrasted with this majority was a small group of Anglo-Cherokee households who exhibited high rates of English literacy and slaveholding, and who managed extensive market farms in the larger river and creek valleys in the southern portion of the study area A relatively small number of fullblood and AngloCherokee families were arrayed between these extremes, forming a heavily skewed socioeconomic continuum largely reflective of household ethnicity. The improved real properties of Cherokee households in southwestern North Carolina are documented by U.S. government property appraisals conducted in the winter of 1836-1837. These appraisals include narrative descriptions and dimensions of dwellings and other buildings, cultivated fields and other cleared or fenced land, fruit trees, ditches, wells, mills, and other facilities present on 684 properties. Hierarchical agglomerative (Ward\u27s method) cluster analysis is used to define types of properties based upon similarities in the values assigned to dwellings, nonresidential structures, and agricultural improvements by the federal appraisers. The resultant cluster solution is interpreted as a series of farmstead models that can be ranked from those more traditional in composition to those more closely resembling Western agrarian modes. These analyses indicate that Cherokee properties in the study area were remarkably homogeneous in composition; more than 85% of the Cherokee farmsteads in southwestern North Carolina consisted of twelve or fewer acres of cropland, small, cribbed log dwellings valued less than $32.00, and few outbuildings other than corn cribs and an occasional asi. Properties owned by a small number of Anglo-Cherokees families contrast sharply with this traditional farmstead mode, and reflect thorough incorporation and integration of Western agrarian material modes of life. The largest and most highly valued Cherokee properties included substantial, hewn log dwellings valued in excess of$70.00, 35 or more acres of cropland, and a wide array of ancillary domestic structures (e.g. kitchens, springhouses, smokehouses), farm buildings (e.g. stables, cribs, barns), and specialized facilities (e.g. stores, mills, blacksmith shops). These farms substantially resembled the typical holdings of Anglo-American middling farmers and small planters in the southern highlands, and the Cherokee owners of such properties occupied a socioeconomic status parallel to the upper middle class of the Anglo-American rural South. A relatively small sector of Anglo-Cherokee and fullblood Cherokee families maintained homes and farms that formed a continuum between these extremes. Contrastive modes of farmstead composition are interpreted as evidence for the operation of distinct Western and traditional systems of household economy and material lifeways. These distinct systems are largely, but not exclusively, correlated with the bioracial and linguistic affinities of Cherokee households, and contrastive farmstead composition is interpreted as evidence for ethnic differentiation among Cherokee households in southwestern North Carolina. Spoliation claims which Cherokees from the study area filed against the United States government following forced removal of 1838 document losses of clothing, furniture, household goods, cookware and tableware, agricultural equipment and other tools, livestock, and other material possessions by more than 400 Cherokee households from the study area. These data are initially explored through univariate comparisons of the distributions of major functional groups of chattel property among bioracial/linguistic subsets of the study population to determine differential patterns of ownership. Hierarchical agglomerative cluster analysis is applied to classify individual household cases by inventory composition. The membership of these groups of households is then evaluated with respect to racial/ethnic affinity to determine whether ethnicity played a significant role in the formation of household assemblages. Analyses of the chattel properties data. reveal patterning similar to that of the real properties data, with a large, homogeneous group of relatively poor, predominantly fullblood families forming the basal economic stratum of Cherokee society contrasted with a small, predominantly English-speaking, group of wealthy Cherokees. A relatively small group of both fullblood and Anglo-Cherokee households span these extremes. These patterns are interpreted as evidence for a traditional-Western continuum in material lifestyles and economic modes; the poles of this continuum appear to represent the contrastive content of an ethnic dichotomy. Archaeological data present a collateral, yet independent gauge of variation in the material lifeways of Removal Period Cherokee households in the study area. To illustrate the differences in material culture that distinguish more Westernized from more traditionally oriented Cherokee households, artifact assemblages representing one Anglo-Cherokee metis occupation, and six fullblood Cherokee household occupations are compared and contrasted in terms of diversity, content, and relative composition. Archaeological assemblages recovered from surface and excavated contexts at these farmstead sites evince a high degree of interhousehold variation in scale and content; this variability is interpreted as evidence of differential acculturation and contrastive cultural orientations. Most of these assemblages are dominated by Qualla series ceramics and other goods reflective of indigenous traditions; these configurations suggest that many of the Cherokee inhabitants of southwestern North Carolina retained strong native identities expressed through continuity of traditional technologies. However, high frequencies of commercially manufactured goods associated with the metis household (the Christies) occupation also indicate substantially higher levels of material wealth and construction of a Westernized material lifestyle informed by AngloAmerican models. which commercial consumption was particularly prominent. These analyses illustrate the broad themes of variation in Cherokee material culture on the eve of the removal of 1838. The extremes of variation evident in these datasets are interpreted as evidence for differential Westernization of Cherokee households, and illustrate the material modes that conservative Cherokees and Westernized Anglo-Cherokees used to define and distinguish their communities of association as nascent ethnic groups struggling over the cultural identity and political fate of the Cherokee Nation

The architecture of Ricardo Porro : questions of form and content

Aside from the two Schools of the Arts built In Cuba during the early sixties, the work of Ricardo Porro is unknown to most American architects. This essay is intended to make available to an American audience a critical examination of Mr. Porro\u27s work. His work consists not only of buildings which have been erected in Cuba, France and Liechtenstein, but also of numerous unbuilt projects. Ricardo Porro is not only an architect but also a painter, sculptor and cabinetmaker. He has also written various articles on architecture which have been published in European journals and, most importantly, he has published two books: Oeuvres/Obras 1950-1993 (Works 1950-1993), which is a portfolio his architecture with descriptions and commentaries, and Les Cinq Aspects Du Contenu (The Five Aspects of Content) which is his theory of architecture. In addition Mr. Porro has implemented his didactic method in his role as professor at various schools of architecture in Cuba, Venezuela, France, and currently in Austria. Hence, Ricardo Porro is active not only as a builder but also in other spheres of architecture. His opinions and beliefs on art and architecture have been made known through his books and in his articles, most of which have been written in French or in Spanish. This author has translated both of his books, Oeuvres/Obras: 1950-1993 and Les Cinq Aspects Du Contenu. These translations are contained in the appendices. Since this is a critical essay of the work of Ricardo Porro--the first to extensively present a critical analysis of his work to date, and certainly the first comprehensive essay about his work to be made available to an English speaking readership--it is advised that the reader become familiar with his work via the drawings, photographs and translations provided for him in the appendix before reading the critical analysis. Recently the internationally circulated architectural journal, Architecture and Urbanism, published an article on the work of Mr. Porro which is valuable for the drawings and color photographs of his projects and for the article entitled, An Architectural Autobiography of Ricardo Porro in the March 1994 Issue. Naturally the best way to get to know his work is to visit his buildings and to hear Porro discuss his views about them. Yet, if one is unable to obtain this direct experience, one must fall back on other less vivid primary sources as a way of getting to know Porro\u27s architecture, namely through drawings, photographs and the articles written by him and about him. The author interviewed Ricardo Porro in his home in Paris, visited his office, and visited three of Mr. Porro\u27s buildings in Paris accompanied by him. Some of the interviews and conversations with the architect were taped. These amount to approximately fifteen hours of conversation covering his views on art and architecture, a discussion of his works and also that of others. These first-hand experiences have been incorporated into the critical analysis. Yet this raw data about Ricardo Porro\u27s work acquired through an investigation of the primary sources cited above is insufficient to bring about a critical examination of his work. Therefore, the literature which has accumulated over the years about Mr. Porro\u27s architecture has been examined. For the most part it seems that the critics\u27s [sic] demonstrate no real understanding of his work on account of their focus on just one project and because of their emphasis on the formal characteristics of his projects without an examination of their content. Many of the articles are merely descriptive and expository. Various attempts have been made by many critics to force him into a category such as organic\u27, \u27expressionist\u27, \u27sculpture-architecture, \u27socialist\u27, etc. Porro\u27s theory of architecture, Les Cinq Aspects Du Contenu, has not been critically commented by architectural historians. Undeniably, the points of view expressed by Ricardo Porro, in his text are crucial for an understanding of his work for it contains the theory upon which he claims his practice is based. It is always the case that in a critical analysis of a work of architecture certain aspects or viewpoints are emphasized at the expense of others. Hence the method adopted to examine a work of architecture will have a preponderant effect on the interpretation of a work. The understanding and appreciation of an architect\u27s work will be quite different if one applies to it a technical interpretation, a social-economic interpretation, philosophical-religious interpretation or any other interpretations which have been used and promulgated by architectural historians and art critics. From these numerous possibilities the author has selected the method and focus which he has found to be most fruitful in giving the reader an understanding of Mr. Porro\u27s total production and to open the way for further inquiries about his work: an analysis of the form and content of the work of Ricardo Porro