A cost-optimal algorithm for guard zone computation including detection and exclusion of overlapping
26 Jun 2015-pp 1-6
TL;DR: This paper has designed a cost-optimal (parallel) algorithm to solve the guard zone computation problem for solving it in distributed environment that finds application in resizing of VLSI circuits.
Abstract: The guard zone G (of width r) of a simple polygon P is a closed region consisting of a set of straight line segments and circular arcs (of radius r) bounding the said polygon such that there exists no pair of points p (on the boundary of P) and q (on the boundary of G) having their Euclidean distance d(p, q) less than the specified value r. In this paper we have designed a cost-optimal (parallel) algorithm to solve the guard zone computation problem for solving it in distributed environment that finds application in resizing of VLSI circuits.
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Book•
31 Jan 1993
TL;DR: This book is a core reference for graduate students and CAD professionals and presents a balance of theory and practice in a intuitive manner.
Abstract: From the Publisher:
This work covers all aspects of physical design. The book is a core reference for graduate students and CAD professionals. For students, concept and algorithms are presented in an intuitive manner. For CAD professionals, the material presents a balance of theory and practice. An extensive bibliography is provided which is useful for finding advanced material on a topic. At the end of each chapter, exercises are provided, which range in complexity from simple to research level.
927 citations
"A cost-optimal algorithm for guard ..." refers background in this paper
...In general, an instance of such a problem may contain thousands of subcircuits at some level of design, and the (placement) problem under consideration is NP-complete [9]....
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...In case of VLSI physical design automation, given a set of isothetic non-overlapping polygonal regions and a common resizing parameter δ, the objective is to compute another set of closed regions resizing each polygon by an amount of δ [9]....
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...In this context, each polygon represents an area and shape of a subcircuit based on its components and interconnection among them when these are assigned on a chip floor, such that several such subcircuits are there for their placement on a minimum area arrangement, placing each pair of adjacent subcircuits in a safe separation, to realize a VLSI circuit or designing an embedded system [9]....
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Book•
01 Dec 1998TL;DR: This chapter discusses the evolution of computer methods for the Handling of Spatial Data, and the role that modelling systems thinking and GIS have in this evolution.
Abstract: 1. What is GIS? 2. Concepts of Space 3. The Evolution of Computer Methods for the Handling of Spatial Data 4. Modelling Systems Thinking and GIS 5. Spatial Data Models 6. Attribute Data Management 7. Data Encoding and Manipulation 8. Data Analysis 9. Data Output 10. Data Quality Issues 11. Organisational Issues 12. Project Design
534 citations
"A cost-optimal algorithm for guard ..." refers background in this paper
...It also finds application in the polygon containment problem and in computing the buffer zone in geographical information systems [5], to name only a few....
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Book•
01 Mar 1997TL;DR: This chapter discusses models of Computation, Combinational Circuits, and Parallel Synergy, which aims to explain the construction of parallel circuits and their applications in medicine and engineering.
Abstract: 1. Introduction2. Models of Computation3. Combinational Circuits4. Parallel Prefix Computation5. Divide and Conquer6. Pointer-Based Data Structures7. Linear Arrays8. Meshes and Related Models9. Hypercubes and Stars10. Models Using Buses11. Broadcasting with Selective Reduction12. Parallel SynergyBibliographyIndex
388 citations
TL;DR: This book is an excellent practical guide in modern parallel scientific programming, and it can be used for self-instruction and also for all specialists who are interested in parallel scientific computing.
Abstract: This textbook on parallel scientific computing presents state-of-the-art material in scientific algorithm design for modem parallel computers. The first volume of this textbook (published in 1986) described the art of scientific computing in Fortran 77 on single-processor syslg, tems. The first edition of the second volume was published in 1996. In the current Second Edition, all codes have been corrected according to version 2.06 of Fortran 90. Volume 2 deals with Fortran 90 compilers, which are now widely available, and is devoted to parallel scientific computing. The book, written with support of the US National Science Foundation, can be very useful for graduate and postgraduate courses and also for all specialists who are interested in parallel scientific computing. It's well known that Fortran is excellent for scientific computing. But in scientific computing, multiprocessor systems are widely used now, instead of single-processor systems. Thus, the actual problem is to modify wellknown recipes according to parallel-programming ideas. This book has successfully solved this problem. First, the authors introduce Fortran 90, parallel programming, and parallel utility functions for Fortran 90. These functions include the move data, returning a location, argument checking and error handling, outer operations on vectors, scatter with combine, skew operations on matrices, polynomials, and recurrences routines. Next, the authors consider the most popular scientific numerical algorithms previously coded in Fortran 77 and present new codes elaborated by Fortran 90 with parallel facilities. They discuss the solution of linear algebra equations, interpolation and extrapolation problems, integration and evaluation of functions, computing of special functions and random numbers, sorting, solution of nonlinear sets of equation and eigenvalue problems, minimization and maximization of functions, Fourier transformation, statistical algorithms, integration of ODE and PDE, and less-numerical algorithms. By studying the presented Fortran 90 parallel codes, readers can get good experience in Fortran 90 and in parallel programming. T o read this book, you only need basic skills in numerical methods and in Fortran programming. Thus, it is an excellent practical guide in modern parallel scientific programming, and it can be used for self-instruction. Unfortunately, the mathematical background of all the algorithms described in the book are only presented in Volume 1. Therefore, to properly study all the routines, the reader must have Volume 1. The book's reference list is not large and contains only about 40 examples of Fortran textbooks, well-known textbooks on numerical methods, and a few books dedicated to parallel programming directly connected with the book's subject. All 3 SO routines considered in the book are available on diskettes or CD ROM for IBM PC, Macintosh, and Unix computers. Readers can purchase this software by mail.
147 citations
"A cost-optimal algorithm for guard ..." refers methods in this paper
...The Minkowski sum is an essential tool for computing the free configuration space of translating a polygonal robot [1]....
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...algorithm, a Concurrent Read Exclusive Write (CREW) Parallel Random Access Machine (PRAM) in a Single Instruction stream Multiple Data stream (SIMD) parallel computing environment [1, 8] has been considered, where a control unit issues an instruction to be executed simultaneously by all processors on their respective data....
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...This parallel sorting operation can be performed in O(log n) time by deploying O(n) number of processors [1]....
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..., for all xi (1 ≤ i ≤ O(n)) along x direction and for all yi (1 ≤ i ≤ O(n)) along y direction, are sorted separately using parallel sorting by merging in O(log n) time having O(n) processors [1]....
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Book•
01 Aug 1993
TL;DR: Inverse Laplace transforms have been used for the integration of trigonometric and hyperbolic functions as discussed by the authors, where the solution of first order differential equations by separation of variables has been studied.
Abstract: Preface Algebra Partial fractions Logarithms Exponential functions Hyperbolic functions Arithmetic and geometric progressions The binomial series Maclaurin's series Solving equations by iterative methods Binary octal and hexadecimal Introduction to trigonometry Cartesian and polar co-ordinates The circle and its properties Trigonometric waveforms Trigonometric identities and equations The relationship between trigonometric and hyperbolic functions Compound angles Functions and their curves Irregular areas volumes and mean values of waveforms Complex numbers De Moivre's theorem The theory of matrices and determinants The solution of simultaneous equations by matrices and determinants Vectors Methods of adding alternating waveforms Scalar and vector products Methods of differentiation Some applications of differentiation Differentiation of parametric equations Differentiation of implicit functions Logarithmic differentiation Differentiation of hyperbolic functions Differentiation of inverse trigonometric and hyperbolic functions Partial differentiation Total differential rates of change and small changes Maxima minima and saddle points for functions of two variables Standard integration Some applications of integration Integration using algebraic substitutions Integration using trigonometric and hyperbolic substitutions Integration using partial fractions The t = __substitution Integration by parts Reduction formulae Numerical integration Solution of first order differential equations by separation of variables Homogeneous first order differential equations Linear first order differential equations Numerical methods for first order differential equations Second order differential equations of the form __ Second order differential equations of the form __ Power series methods of solving ordinary differential equations An introduction to partial differential equations Presentation of statistical data Measures of central tendency and dispersion Probability The binomial and Poisson distributions The normal distribution Linear correlation Linear regression Introduction to Laplace transforms Properties of Laplace transforms Inverse Laplace transforms The solution of differential equations using Laplace transforms The solution of simultaneous differential equations using Laplace transforms Fourier series for periodic functions of period 2p Fourier series for a non-periodic function over range 2p Even and odd functions and half-range Fourier series Fourier series over any range A numerical method of harmonic analysis The complex or exponential form of a Fourier series Essential formulae Index
121 citations