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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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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 17 (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.
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 10 (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...
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.
Assessing probabilistic timing constraints on system performance. Design Automation for Embedded Systems
, 2000
"... Abstract. We propose an algorithm for assessing probabilistic timing constraints for systems including components with uncertain delays. We make a case for designing systems based on a probabilistic relaxation of such constraints, as this has the potential for resulting in lower silicon area and/or ..."
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Abstract. We propose an algorithm for assessing probabilistic timing constraints for systems including components with uncertain delays. We make a case for designing systems based on a probabilistic relaxation of such constraints, as this has the potential for resulting in lower silicon area and/or power consumption. We consider a concrete example, an MPEG decoder, for which we discuss modeling and assessment of probabilistic throughput constraints.
Persistence in Discrete Optimization under Data Uncertainty
, 2004
"... An important question in discrete optimization under uncertainty is to understand the persistency of a decision variable, i.e., the probability that it is part of an optimal solution. For instance, in project management, when the task activity times are random, the challenge is to determine a set o ..."
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An important question in discrete optimization under uncertainty is to understand the persistency of a decision variable, i.e., the probability that it is part of an optimal solution. For instance, in project management, when the task activity times are random, the challenge is to determine a set of critical activities that will potentially lie on the longest path. In the spanning tree and shortest path network problems, when the arc lengths are random, the challenge is to preprocess the network and determine a smaller set of arcs that will most probably be a part of the optimal solution under different realizations of the arc lengths. Building on a characterization of moment cones for single variate problems, and its associated semidefinite constraint representation, we develop a limited marginal moment model to compute the persistency of a decision variable. Under this model, we show that finding the persistency is tractable for zeroone optimization problems with a polynomial sized representation of the convex hull of the feasible region. Through extensive experiments, we show that the persistency computed under the limited marginal moment model is often close to the simulated persistency value under various distributions that satisfy the prescribed marginal moments and are generated independently.
1 Activity Networks and Uncertainty Quantification: 2 nd Order Probability for Solving Graphs of Concurrent and Sequential Tasks
"... Abstract. Activity networks model the time to project completion based on the times to complete various subtasks, some of which can proceed concurrently and others of which are prerequisite to others. Uncertainty in the times to complete subtasks implies uncertainty in the overall time to complete t ..."
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Abstract. Activity networks model the time to project completion based on the times to complete various subtasks, some of which can proceed concurrently and others of which are prerequisite to others. Uncertainty in the times to complete subtasks implies uncertainty in the overall time to complete the project. When the information about the times to complete subtasks is insufficient to fully specify a probability distribution but sufficient to bound the distribution, the problem of making conclusions about time to complete the entire project requires use of secondorder probabilistic techniques. An intervalbased technique for this is described, and applied to the problem of evaluating activity networks. 1.
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
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.
Criticality analysis of activity networks under interval uncertainty
"... This paper reconsiders the PERT scheduling problem when information about task duration is incomplete. We model uncertainty on task durations by intervals. With this problem formulation, our goal is to assert possible and necessary criticality of the different tasks and to compute their possible ea ..."
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This paper reconsiders the PERT scheduling problem when information about task duration is incomplete. We model uncertainty on task durations by intervals. With this problem formulation, our goal is to assert possible and necessary criticality of the different tasks and to compute their possible earliest starting dates, latest starting dates and floats. This paper puts together various results and provides a complete solution to the problem. We present the complexity results of all considered subproblems and efficient algorithms to solve them.