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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 27 (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.
A Computational Study on Bounding the Makespan Distribution in Stochastic Project Networks
 ANNALS OF OPERATIONS RESEARCH
, 1998
"... Given a stochastic project network with independently distributed activity durations, several approaches to bound the distribution function of the project completion time have been proposed. We have implemented the most promising of these algorithms and compare their behavior on a basis of nearly 20 ..."
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Cited by 14 (1 self)
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Given a stochastic project network with independently distributed activity durations, several approaches to bound the distribution function of the project completion time have been proposed. We have implemented the most promising of these algorithms and compare their behavior on a basis of nearly 2000 instances with up to 1200 activities of different testbeds. We propose a suitable numerical representation of the given distributions which is the basis for excellent computational results.
Probabilistic Arithmetic
, 1989
"... This thesis develops the idea of probabilistic arithmetic. The aim is to replace arithmetic operations on numbers with arithmetic operations on random variables. Specifically, we are interested in numerical methods of calculating convolutions of probability distributions. The longterm goal is to ..."
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Cited by 13 (0 self)
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This thesis develops the idea of probabilistic arithmetic. The aim is to replace arithmetic operations on numbers with arithmetic operations on random variables. Specifically, we are interested in numerical methods of calculating convolutions of probability distributions. The longterm goal is to be able to handle random problems (such as the determination of the distribution of the roots of random algebraic equations) using algorithms which have been developed for the deterministic case. To this end, in this thesis we survey a number of previously proposed methods for calculating convolutions and representing probability distributions and examine their defects. We develop some new results for some of these methods (the Laguerre transform and the histogram method), but ultimately find them unsuitable. We find that the details on how the ordinary convolution equations are calculated are
A heuristic for optimizing stochastic activity networks with applications to statistical digital circuit sizing
 IEEE Transactions on Circuits and SystemsI
, 2004
"... A deterministic activity network (DAN) is a collection of activities, each with some duration, along with a set of precedence constraints, which specify that activities begin only when certain others have finished. One critical performance measure for an activity network is its makespan, which is th ..."
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Cited by 12 (4 self)
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A deterministic activity network (DAN) is a collection of activities, each with some duration, along with a set of precedence constraints, which specify that activities begin only when certain others have finished. One critical performance measure for an activity network is its makespan, which is the minimum time required to complete all activities. In a stochastic activity network (SAN), the durations of the activities and the makespan are random variables. The analysis of SANs is quite involved, but can be carried out numerically by Monte Carlo analysis. This paper concerns the optimization of a SAN, i.e., the choice of some design variables that affect the probability distributions of the activity durations. We concentrate on the problem of minimizing a quantile (e.g., 95%) of the makespan, subject to constraints on the variables. This problem has many applications, ranging from project management to digital integrated circuit (IC) sizing (the latter being our motivation). While there are effective methods for optimizing DANs, the SAN optimization problem is much more difficult; the few existing methods cannot handle largescale problems.
A Survey on Solution Methods for Task Graph Models
, 1993
"... We give in this paper a survey on models developed in the literature using the concept of task graphs, focusing on solution techniques. Different types of task graphs are considered, from PERTS networks to random task graphs. Reviewed solution methods include exact computations and bounds. 1 Int ..."
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Cited by 9 (4 self)
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We give in this paper a survey on models developed in the literature using the concept of task graphs, focusing on solution techniques. Different types of task graphs are considered, from PERTS networks to random task graphs. Reviewed solution methods include exact computations and bounds. 1 Introduction, Concepts and Notations The purpose of this paper is to survey models based on stochastic task graph representations and the solutions techniques that have been developed for them. The reason for doing this in the framework of the QMIPS project is that task graphs appear to be of central importance in the modeling and analysis of parallel programs and architectures. Yet, the solution of task graph problems is difficult in general. No really satisfactory and sufficiently general solutions have been proposed as of today, and research is still active in the area. The term "task graphs" covers now a wide variety of models. We shall begin the survey with what appears to be the initi...
Probabilistic combinatorial optimization: Moments, semidefinite programming and asymptotic bounds
 SIAM Journal on Optimization
, 2003
"... Abstract. We address the problem of evaluating the expected optimal objective value of a 01 optimization problem under uncertainty in the objective coefficients. The probabilistic model we consider prescribes limited marginal distribution information for the objective coefficients in the form of mo ..."
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Cited by 6 (2 self)
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Abstract. We address the problem of evaluating the expected optimal objective value of a 01 optimization problem under uncertainty in the objective coefficients. The probabilistic model we consider prescribes limited marginal distribution information for the objective coefficients in the form of moments. We show that for a fairly general class of marginal information, a tight upper (lower) bound on the expected optimal objective value of a 01 maximization (minimization) problem can be computed in polynomial time if the corresponding deterministic problem is solvable in polynomial time. We provide an efficiently solvable semidefinite programming formulation to compute this tight bound. We also analyze the asymptotic behavior of a general class of combinatorial problems that includes the linear assignment, spanning tree, and traveling salesman problems, under knowledge of complete marginal distributions, with and without independence. We calculate the limiting constants exactly.
A Study of Approximating the Moments of the Job Completion Time in PERT Networks
, 1995
"... this paper. The project starts at the initial node and ends at the terminal node. A path is a set of nodes connected by arrows which begin at the initial node and end at the terminal node. This collection of arcs, nodes and paths is collectively called an activity network. A project is deemed comple ..."
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Cited by 4 (0 self)
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this paper. The project starts at the initial node and ends at the terminal node. A path is a set of nodes connected by arrows which begin at the initial node and end at the terminal node. This collection of arcs, nodes and paths is collectively called an activity network. A project is deemed complete if work along all paths is complete. After the development of the network, the next major planning step is the estimation of activity and project times. Typical methods for estimating activity times have been to use point estimates or some sort of range or distribution. The type of method used depends on the situation facing the project manager. Hershauer and Nabielsky (1972) categorize the situations into three major categories, viz., certainty, risk, and uncertainty. They further subdivide these categories based on availability of knowledge regarding the mode, range and distribution of the time estimates. They then map the situation and estimations to the appropriate methods to be adopted. If activity times are deterministic, the duration of the project completion time is determined by the length of the longest path in the network. However, this becomes complicated when activity times are stochastic in nature. We assume a scenario equivalent to Hershauer and Nabielsky's risk categorynamely, a common distribution situation. For a stochastic activity network, Kulkarni and Adlakha (1986) have identified three important measures of performance: (a) Distribution of the project completion time.
An efficient Activity Network Reduction Algorithm based on the Label Correcting Tracing Algorithm
"... Abstract—When faced with stochastic networks with an uncertain duration for their activities, the securing of network completion time becomes problematical, not only because of the nonidentical pdf of duration for each node, but also because of the interdependence of network paths. As evidenced by ..."
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Abstract—When faced with stochastic networks with an uncertain duration for their activities, the securing of network completion time becomes problematical, not only because of the nonidentical pdf of duration for each node, but also because of the interdependence of network paths. As evidenced by Adlakha & Kulkarni [1], many methods and algorithms have been put forward in attempt to resolve this issue, but most have encountered this same largesize network problem. Therefore, in this research, we focus on network reduction through a Series/Parallel combined mechanism. Our suggested algorithm, named the Activity Network Reduction Algorithm (ANRA), can efficiently transfer a largesize network into an S/P Irreducible Network (SPIN). SPIN can enhance stochastic network analysis, as well as serve as the judgment of symmetry for the Graph Theory.
Diffusion Activity Networks
, 1999
"... An activity network (AN) is a directed acyclic graph with n nodes and A arcs. The nodes are numbered from 1 to n so that an arc always leads from a smaller numbered node to a higher numbered node. The graph has only one node with no incident arcs, which is called the starting node and numbered 1. No ..."
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An activity network (AN) is a directed acyclic graph with n nodes and A arcs. The nodes are numbered from 1 to n so that an arc always leads from a smaller numbered node to a higher numbered node. The graph has only one node with no incident arcs, which is called the starting node and numbered 1. Node n is the only node with no emanating arcs and is named the terminal node. An arc represents an activity and a node the start or the culmination of that activity. The terminal node represents the end of the project. These kinds ofgraphsarealsoreferredtoasActivity on Arc (AoA) representation of AN. In DiAN the process represented by the arcs is a diffusion process, the state of which is identified with the remaining work content (rwc). The process starts at time ‘0 ’ at rwc = 1 with a negative drift coefficient. An absorbing barrier is placed at rwc = 0 to identify with the end of the process. The completion time of an activity is thus the first passage time of such a diffusion process. The paradigm of DiAN, while offering an enhanced modeling concept, raises many questions regarding computational challenges, definition of project management metrics and applicability of such a tool in areas beyond project management. The thesis primarily focuses
SOLVING STOCHASTIC PERT NETWORKS EXACTLY USING HYBRID BAYESIAN NETWORKS
"... In this paper, we describe how a stochastic PERT network can be formulated as a Bayesian network. We approximate such PERT Bayesian network by mixtures of Gaussians hybrid Bayesian networks. Since there exists algorithms for solving mixtures of Gaussians hybrid Bayesian networks exactly, we can use ..."
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In this paper, we describe how a stochastic PERT network can be formulated as a Bayesian network. We approximate such PERT Bayesian network by mixtures of Gaussians hybrid Bayesian networks. Since there exists algorithms for solving mixtures of Gaussians hybrid Bayesian networks exactly, we can use these algorithms to make inferences in PERT Bayesian networks. 1