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Fast and Exact Simultaneous Gate and Wire Sizing by Lagrangian Relaxation
 In Proceedings of the 1998 IEEE/ACM international conference on Computeraided design
, 1997
"... This paper considers simultaneous gate and wire sizing for general VLSI circuits under the Elmore delay model. We present a fast and exact algorithm which can minimize total area subject to maximum delay bound. The algorithm can be easily modified to give exact algorithms for optimizing several othe ..."
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Cited by 80 (8 self)
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This paper considers simultaneous gate and wire sizing for general VLSI circuits under the Elmore delay model. We present a fast and exact algorithm which can minimize total area subject to maximum delay bound. The algorithm can be easily modified to give exact algorithms for optimizing several other objectives (e.g. minimizing maximum delay or minimizing total area subject to arrival time specifications at all inputs and outputs). No previous algorithm for simultaneous gate and wire sizing can guarantee exact solutions for general circuits. Our algorithm is an iterative one with a guarantee on convergence to global optimal solutions. It is based on Lagrangian relaxation and "onegate/wireatatime" local optimizations, and is extremely economical and fast. For example, we can optimize a circuit with 13824 gates and wires in about 13 minutes using under 12 MB memory on an IBM RS/6000 workstation. 1 Introduction Since the invention of integrated circuits almost 40 years ago, gate si...
Optimal design of a CMOS opamp via geometric programming
 IEEE Transactions on ComputerAided Design
, 2001
"... We describe a new method for determining component values and transistor dimensions for CMOS operational ampli ers (opamps). We observe that a wide variety of design objectives and constraints have a special form, i.e., they are posynomial functions of the design variables. As a result the ampli er ..."
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Cited by 51 (10 self)
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We describe a new method for determining component values and transistor dimensions for CMOS operational ampli ers (opamps). We observe that a wide variety of design objectives and constraints have a special form, i.e., they are posynomial functions of the design variables. As a result the ampli er design problem can be expressed as a special form of optimization problem called geometric programming, for which very e cient global optimization methods have been developed. As a consequence we can e ciently determine globally optimal ampli er designs, or globally optimal tradeo s among competing performance measures such aspower, openloop gain, and bandwidth. Our method therefore yields completely automated synthesis of (globally) optimal CMOS ampli ers, directly from speci cations. In this paper we apply this method to a speci c, widely used operational ampli er architecture, showing in detail how to formulate the design problem as a geometric program. We compute globally optimal tradeo curves relating performance measures such as power dissipation, unitygain bandwidth, and openloop gain. We show how the method can be used to synthesize robust designs, i.e., designs guaranteed to meet the speci cations for a
Bandwidth Extension in CMOS with Optimized OnChip Inductors
 IEEE Journal of SolidState Circuits
, 2000
"... We present a technique for enhancing the bandwidth of gigahertz broadband circuitry by using optimized onchip spiral inductors as shuntpeaking elements. The series resistance of the onchip inductor is incorporated as part of the load resistance to permit a large inductance to be realized with mi ..."
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Cited by 12 (3 self)
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We present a technique for enhancing the bandwidth of gigahertz broadband circuitry by using optimized onchip spiral inductors as shuntpeaking elements. The series resistance of the onchip inductor is incorporated as part of the load resistance to permit a large inductance to be realized with minimum area and capacitance. Simple, accurate inductance expressions are used in a lumped circuit inductor model to allow the passive and active components in the circuit to be simultaneously optimized. A quick and efficient global optimization method, based on geometric programming, is discussed. The bandwidth extension technique is applied in the implementation of a 2.125Gbaud preamplifier that employs a commongate input stage followed by a cascoded commonsource stage. Onchip shunt peaking is introduced at the dominant pole to improve the overall system performance, including a 40% increase in the transimpedance. This implementation achieves a 1.6k\Omega transimpedance and a 0.6 A i...
An efficient and optimal algorithm for simultaneous buffer and wire sizing
 IEEE Trans. ComputerAided Design
, 1999
"... Abstract—In this paper, we consider the problem of interconnect delay minimization by simultaneous buffer and wire sizing under the Elmore delay model. We first present a polynomial time algorithm SBWS to minimize the delay of an interconnect wire. Previously, no polynomial time algorithm for the pr ..."
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Cited by 11 (0 self)
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Abstract—In this paper, we consider the problem of interconnect delay minimization by simultaneous buffer and wire sizing under the Elmore delay model. We first present a polynomial time algorithm SBWS to minimize the delay of an interconnect wire. Previously, no polynomial time algorithm for the problem has been reported in the literature. SBWS is an iterative algorithm with guaranteed convergence to the optimal solution. It runs in quadratic time and uses constant memory for computation. Experimental results show that SBWS is extremely efficient in practice. For example, for an interconnect of 10 000 segments and buffers, the CPU time is only 0.255 s. We then extend our result to handle interconnect trees. We present an algorithm SBWST which always gives the optimal solution. Experimental results show that SBWST is faster than the greedy wire sizing algorithm [2] in practice. Index Terms — Buffer sizing, interconnect, performance optimization, physical design, wire sizing.
A general approach to sparse basis selection: Majorization, concavity, and affine scaling
 IN PROCEEDINGS OF THE TWELFTH ANNUAL CONFERENCE ON COMPUTATIONAL LEARNING THEORY
, 1997
"... Measures for sparse best–basis selection are analyzed and shown to fit into a general framework based on majorization, Schurconcavity, and concavity. This framework facilitates the analysis of algorithm performance and clarifies the relationships between existing proposed concentration measures use ..."
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Cited by 6 (3 self)
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Measures for sparse best–basis selection are analyzed and shown to fit into a general framework based on majorization, Schurconcavity, and concavity. This framework facilitates the analysis of algorithm performance and clarifies the relationships between existing proposed concentration measures useful for sparse basis selection. It also allows one to define new concentration measures, and several general classes of measures are proposed and analyzed in this paper. Admissible measures are given by the Schurconcave functions, which are the class of functions consistent with the socalled Lorentz ordering (a partial ordering on vectors also known as majorization). In particular, concave functions form an important subclass of the Schurconcave functions which attain their minima at sparse solutions to the best basis selection problem. A general affine scaling optimization algorithm obtained from a special factorization of the gradient function is developed and proved to converge to a sparse solution for measures chosen from within this subclass.
Maximum Likelihood Estimation: A Single and Multiobjective Entropy Optimization Approach
"... Abstract: In this paper we first considered a maximum likelihood estimation of trip distribution problem and next use primaldual geometric programming method the said trip distribution problem converted into an entropy maximization trip distribution problem. Here the generalized cost function is as ..."
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Abstract: In this paper we first considered a maximum likelihood estimation of trip distribution problem and next use primaldual geometric programming method the said trip distribution problem converted into an entropy maximization trip distribution problem. Here the generalized cost function is assumed in different form, and then the said formulation is equivalent to single or multiobjective entropy maximization trip distribution problem. We use fuzzy mathematical programming method to show this equivalent problem formulation. The present article we use the concept of multiobjective trip distribution problem.
A Fast Algorithm for Optimal WireSizing Under Elmore Delay Model
 In Proc. IEEE ISCAS
, 1996
"... In this paper, we present a fast algorithm for continuous wiresizing under the distributed Elmore delay model. Our algorithm GWSAC is an extension of the GWSA algorithm (for discrete wiresizing) in [CL93a]. GWSAC is an iterative algorithm with guaranteed convergence to optimal wiresizing soluti ..."
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In this paper, we present a fast algorithm for continuous wiresizing under the distributed Elmore delay model. Our algorithm GWSAC is an extension of the GWSA algorithm (for discrete wiresizing) in [CL93a]. GWSAC is an iterative algorithm with guaranteed convergence to optimal wiresizing solutions. When specialized to discrete wiresizing problems, GWSAC is an improved implementation of GWSA, both in terms of runtime and memory usage. GWSAC is extremely fast even on very large problems. For example, we can solve a 1,000,000 wiresegment problem in less than 3 minutes runtime on an IBM RS/6000 workstation. This kind of efficiency in wiresizing has never been reported in the literature. 1 Introduction Since interconnect delay has become the dominant factor of circuit delay in deep submicron fabrication technology, it is clear that sizing the gates alone is not enough to achieve desirable circuit performance. As a result, wiresizing for performance optimization is currently a v...
Geometric Programming Problems with Fuzzy Parameters and its Application to Crane Load Sway 1
"... Abstract: In this work an approach is proposed to solve geometric programming problems under uncertainty. The proposed approach derives the lower and upper bounds of the objective of geometric programming problems with fuzzy parameters. A pair of twolevel mathematical programs is formulated to calc ..."
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Abstract: In this work an approach is proposed to solve geometric programming problems under uncertainty. The proposed approach derives the lower and upper bounds of the objective of geometric programming problems with fuzzy parameters. A pair of twolevel mathematical programs is formulated to calculate the lower and upper bounds of the objective value. The solution is in a range. Two illustrative examples are presented to clarify the proposed approach. The problem of suppressing the crane load sway has been also considered as a practical application to illustrate the effectiveness of the proposed approach. Key words: Optimization • geometric programming • fuzzy parameters • duality theorem • crane load sway
Optimal Power Control in InterferenceLimited Fading Wireless Channels With OutageProbability Specifications
"... Abstract—We propose a new method of power control for interferencelimited wireless networks with Rayleigh fading of both the desired and interference signals. Our method explictly takes into account the statistical variation of both the received signal and interference power and optimally allocates ..."
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Abstract—We propose a new method of power control for interferencelimited wireless networks with Rayleigh fading of both the desired and interference signals. Our method explictly takes into account the statistical variation of both the received signal and interference power and optimally allocates power subject to constraints on the probability of fading induced outage for each transmitter/receiver pair. We establish several results for this type of problem. We establish tight bounds that relate the outage probability caused by channel fading to the signaltointerference margin calculated when the statistical variation of the signal and intereference powers is ignored. This allows us to show that wellknown methods for allocating power, based on Perron–Frobenius eigenvalue theory, can be used to determine power allocations that are provably close to achieving optimal (i.e., minimal) outage probability. We show that the problems of minimizing transmitter power subject to constraints on outage probability and minimizing outage probability subject to power constraints can be posed as a geometric program (GP). A GP is a special type of optimization problem that can be transformed to a nonlinear convex optimization problem by a change of variables and therefore solved globally and efficiently by recently developed interiorpoint methods. We also give a fast iterative method for finding the optimal power allocation to minimize outage probability. Index Terms—Fading channels, personal communication networks, power control, radio communication. I.