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115
Performance optimization of VLSI interconnect layout
 Integration, the VLSI Journal
, 1996
"... This paper presents a comprehensive survey of existing techniques for interconnect optimization during the VLSI physical design process, with emphasis on recent studies on interconnect design and optimization for highperformance VLSI circuit design under the deep submicron fabrication technologies. ..."
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Cited by 117 (32 self)
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This paper presents a comprehensive survey of existing techniques for interconnect optimization during the VLSI physical design process, with emphasis on recent studies on interconnect design and optimization for highperformance VLSI circuit design under the deep submicron fabrication technologies. First, we present a number of interconnect delay models and driver/gate delay models of various degrees of accuracy and efficiency which are most useful to guide the circuit design and interconnect optimization process. Then, we classify the existing work on optimization of VLSI interconnect into the following three categories and discuss the results in each category in detail: (i) topology optimization for highperformance interconnects, including the algorithms for total wire length minimization, critical path length minimization, and delay minimization; (ii) device and interconnect sizing, including techniques for efficient driver, gate, and transistor sizing, optimal wire sizing, and simultaneous topology construction, buffer insertion, buffer and wire sizing; (iii) highperfbrmance clock routing, including abstract clock net topology generation and embedding, planar clock routing, buffer and wire sizing for clock nets, nontree clock routing, and clock schedule optimization. For each method, we discuss its effectiveness, its advantages and limitations, as well as its computational efficiency. We group the related techniques according to either their optimization techniques or optimization objectives so that the reader can easily compare the quality and efficiency of different solutions.
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 105 (9 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
"... We describe a new method for determining component values and transistor dimensions for CMOS operational amplifiers (opamps). We observe that a wide variety of design objectives and constraints have a special form, i.e., theyareposynomial functions of the design variables. As a result the amplifi ..."
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Cited by 85 (9 self)
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We describe a new method for determining component values and transistor dimensions for CMOS operational amplifiers (opamps). We observe that a wide variety of design objectives and constraints have a special form, i.e., theyareposynomial functions of the design variables. As a result the amplifier design problem can be expressed as a special form of optimization problem called geometric programming, for which very efficient global optimization methods have been developed. As a consequence we can efficiently determine globally optimal amplifier designs, or globally optimal tradeoffs among competing performance measures such as power, openloop gain, and bandwidth. Our method therefore yields completely automated synthesis of (globally) optimal CMOS amplifiers, directly from specifications. In this paper we apply this method to a specific, widely used operational amplifier architecture, showing in detail how to formulate the design problem as a geometric program. We compute globally optimal tradeoff 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 specifications for a variety of process conditions and parameters.
Gate Sizing for Constrained delay/power/area optimization
 in IEEE Transcation on VLSI Design
, 1997
"... Abstract—Gate sizing has a significant impact on the delay, power dissipation, and area of the final circuit. It consists of choosing for each node of a mapped circuit a gate implementation in the library so that a cost function is optimized under some constraints. For instance, one wants to mini ..."
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Cited by 42 (1 self)
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Abstract—Gate sizing has a significant impact on the delay, power dissipation, and area of the final circuit. It consists of choosing for each node of a mapped circuit a gate implementation in the library so that a cost function is optimized under some constraints. For instance, one wants to minimize the power consumption and/or the area of a circuit under some userdefined delay constraints, or to obtain the fastest circuit within a given power budget. Although this technologydependent optimization has been investigated for years, the proposed approaches sometimes rely on assumptions, cost models, or algorithms that make them unrealistic or impossible to apply on reallife large circuits. We discusse here a gate sizing algorithm (GS), and show how it is used to achieve constrained optimization. It can be applied on large circuits within a reasonable CPU time, e.g., minimizing the power of a 10000 nodes circuit under some delay constraint in 2 hours. Keywords—Gate sizing, discrete constrained optimization, delay/power/area tradeoff I.
Digital Circuit Optimization via Geometric Programming
 Operations Research
, 2005
"... informs ® doi 10.1287/opre.1050.0254 © 2005 INFORMS This paper concerns a method for digital circuit optimization based on formulating the problem as a geometric program (GP) or generalized geometric program (GGP), which can be transformed to a convex optimization problem and then very efficiently s ..."
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Cited by 42 (7 self)
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informs ® doi 10.1287/opre.1050.0254 © 2005 INFORMS This paper concerns a method for digital circuit optimization based on formulating the problem as a geometric program (GP) or generalized geometric program (GGP), which can be transformed to a convex optimization problem and then very efficiently solved. We start with a basic gate scaling problem, with delay modeled as a simple resistorcapacitor (RC) time constant, and then add various layers of complexity and modeling accuracy, such as accounting for differing signal fall and rise times, and the effects of signal transition times. We then consider more complex formulations such as robust design over corners, multimode design, statistical design, and problems in which threshold and power supply voltage are also variables to be chosen. Finally, we look at the detailed design of gates and interconnect wires, again using a formulation that is compatible with GP or GGP.
New Algorithms for Gate Sizing: A Comparative Study
 IN DAC
, 1996
"... Gate sizing consists of choosing for each node of a mapped network a gate implementation in the library so that some cost function is optimized under some constraints. It has a significant impact on the delay, power dissipation, and area of the final circuit. This paper compares five gate sizing alg ..."
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Cited by 40 (1 self)
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Gate sizing consists of choosing for each node of a mapped network a gate implementation in the library so that some cost function is optimized under some constraints. It has a significant impact on the delay, power dissipation, and area of the final circuit. This paper compares five gate sizing algorithms targeting discrete, nonlinear, nonunimodal, constrained optimization. The goal is to overcome the nonlinearity and nonunimodality of the delay and the power to achieve good quality results within a reasonable CPU time, e.g., handling a 10000 node network in 2 hours. We compare the five algorithms on constraint free delay optimization and delay constrained power optimization, and show that one method is superior to the others.
Power Modeling and Characteristics of Field Programmable Gate Arrays
, 2005
"... This paper studies power modeling for Field Programmable ..."
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Cited by 38 (9 self)
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This paper studies power modeling for Field Programmable
Gate Sizing Using Incremental Parameterized Statistical Timing Analysis
 In ICCAD
, 2005
"... Abstract — As technology scales into the sub90nm domain, manufacturing variations become an increasingly significant portion of circuit delay. As a result, delays must be modeled as statistical distributions during both analysis and optimization. This paper uses incremental, parametric statistical ..."
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Cited by 36 (2 self)
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Abstract — As technology scales into the sub90nm domain, manufacturing variations become an increasingly significant portion of circuit delay. As a result, delays must be modeled as statistical distributions during both analysis and optimization. This paper uses incremental, parametric statistical static timing analysis (SSTA) to perform gate sizing with a required yield target. Both correlated and uncorrelated process parameters are considered by using a firstorder linear delay model with fitted process sensitivities. The fitted sensitivities are verified to be accurate with circuit simulations. Statistical information in the form of criticality probabilities are used to actively guide the optimization process which reduces runtime and improves area and performance. The gate sizing results show a significant improvement in worst slack at 99.86 % yield over deterministic optimization. I.
A New Statistical Optimization Algorithm for Gate Sizing
"... In this paper, we approach the gate sizing problem in VLSI circuits in the context of increasing variability of process and circuit parameters as technology scales into the nanometer regime. We present a statistical sizing approach that takes into account randomness in gate delays by formulating a ..."
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Cited by 29 (2 self)
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In this paper, we approach the gate sizing problem in VLSI circuits in the context of increasing variability of process and circuit parameters as technology scales into the nanometer regime. We present a statistical sizing approach that takes into account randomness in gate delays by formulating a robust linear program that can be solved efficiently. We demonstrate the efficiency and computational tractability of the proposed algorithm on the various ISCAS’85 benchmark circuits. Across the benchmarks, compared to the deterministic approach, the power savings range from 23 − 30 % for the same timing target and the yield level, the average power saving being 28%. The runtime is reasonable, ranging from a few seconds to around 10 mins, and grows linearly.
GradientBased Optimization of Custom Circuits Using a StaticTiming Formulation
, 1999
"... This paper describes a method of optimally sizing digital circuits on a statictiming basis. All paths through the logic are considered simultaneously and no input patterns need be specified by the user. The method is unique in that it is based on gradientbased, nonlinear optimization and can accom ..."
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Cited by 28 (4 self)
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This paper describes a method of optimally sizing digital circuits on a statictiming basis. All paths through the logic are considered simultaneously and no input patterns need be specified by the user. The method is unique in that it is based on gradientbased, nonlinear optimization and can accommodate transistorlevel schematics without the need for precharacterization. It employs efficient timedomain simulation and gradient computation for each channelconnected component. A largescale, generalpurpose, nonlinear optimization package is used to solve the tuning problem. A prototype tuner has been developed that accommodates combinational circuits consisting of parameterized library cells. Numerical results are presented.