16215317
Large-scale placement by grid-warping
Grid-warping is a new placement algorithm based on a strikingly simple idea: rather than move the gates to optimize their location, we elastically deform a model of the 2-D chip surface on which the gates have been roughly placed, "stretching" it until the gates arrange themselves to our liking. Put simply: we move the grid, not the gates. Deforming the elastic grid is a surprisingly simple, low-dimensional nonlinear optimization, and augments a traditional quadratic formulation. A preliminary implementation, WARP1, is already competitive with most recently published placers, e.g., placements that average 4% better wirelength, 40% faster than GORDIAN-L-DOMINO.
61488328
Interval-valued reduced order statistical interconnect modeling
We show how recent advances in the handling of correlated interval representations of range uncertainty can be used to predict the impact of statistical manufacturing variations on linear interconnect. We represent correlated statistical variations in RLC parameters as sets of correlated intervals, and show how classical model order reduction methods - AWE and PRIMA - can be re-targeted to compute interval-valued, rather than scalar-valued reductions. By applying a statistical interpretation and sampling to the resulting compact interval-valued model, we can efficiently estimate the impact of variations on the original circuit. Results show the technique can predict mean delay with errors between 5-10%, for correlated RLC parameter variations up to 35%.
10392733
Pre-routing estimation of shielding for RLC signal integrity
The formula-based K/sub eff/ model is a figure of merit for inductive coupling, and has been used to solve the simultaneous shield insertion and net ordering (SINO) and simultaneous signal and power routing (SPR) problems. The authors first show that the K/sub eff/ model has a high fidelity compared to the SPICE-computed noise under an accurate RLC circuit model. We then develop simple yet accurate formulae to estimate numbers of shields needed by optimal SINO solutions under the K/sub eff/ model. Extensive experiments show that our pre-routing estimation has errors less than 10% compared to solutions given by detailed SINO algorithms. These formulae can be used effectively as a pre-routing congestion estimation for layout planning and synthesis.
956305
Fast interval-valued statistical modeling of interconnect and effective capacitance
Correlated interval representations of range uncertainty offer an attractive solution to approximating computations on statistical quantities. The key idea is to use finite intervals to approximate the essential mass of a probability density function (pdf) as it moves through numerical operators; the resulting compact interval-valued solution can be easily interpreted as a statistical distribution and efficiently sampled. This paper first describes improved interval-valued algorithms for asymptotic wave evaluation (AWE)/passive reduced-order interconnect macromodeling algorithm (PRIMA) model order reduction for tree-structured interconnect circuits with correlated resistance, inductance, and capacitance (RLC) parameter variations. By moving to a much faster interval-valued linear solver based on path-tracing ideas, and making more optimal tradeoffs between interval- and scalar-valued computations, the delay statistics roughly 10/spl times/ faster than classical Monte Carlo (MC) simulation, with accuracy to within 5% can be extracted. This improved interval analysis strategy is further applied in order to build statistical effective capacitance (C/sub eff/) models for variational interconnect, and show how to extract statistics of C/sub eff/ over 100/spl times/ faster than classical MC simulation, with errors less than 4%.
1826840
Towards global routing with RLC crosstalk constraints
Conventional global routing minimizes total wire length and congestion. Experiments using large industrial benchmark circuits show that up to 24% of nets in such routing solutions may have RLC crosstalk violations at 3GHz clock. We develop an extremely efficient length-scaled Keff (LSK) model that has a high fidelity for long-range RLC crosstalk. We formulate an extended global routing problem (denoted as GSINO) to consider simultaneous shield insertion and net ordering with RLC crosstalk constraints, then propose an effective three-phase GSINO algorithm. The GSINO algorithm completely eliminates the RLC crosstalk violations, and has small area and wire length overhead compared to conventional routing.
2749728
Interval-valued statistical modeling of oxide chemical-mechanical polishing
Technology-oriented tools provide the raw data needed to optimize the fabrication process itself, and to predict problematic variational impacts on silicon design. Unfortunately, even in these physics-oriented tools, statistically uncertain quantities appear as crucial inputs. To date, Monte Carlo techniques have been the dominant solution method. We suggest an alternative in which uncertainties are represented as correlated intervals, and interval-valued computations replace the standard scalar operations in the numerical algorithm for the tool. We use an oxide chemical-mechanical polishing tool as an example, and show how to "retrofit" workable statistical models on top of the original algorithm. Accuracies to within /spl sim/1-10% of Monte Carlo simulation, and speedups of /spl sim/10-100X can be achieved, depending on whether we choose a formulation which emphasizes accuracy, or efficiency.
2850355
An Optimal Node Selection Scheme in Multi-hop Wireless Network
In this paper, a cooperative wireless multi-hop network is considered, cooperative diversity can be realized by allowing nodes close proximity to cooperate in transmission. In order to group receiver nodes into a cluster, it is necessary to select appropriate nodes. We introduce an optimal node selection algorithm based on MIMO antenna selection, this algorithm, combining with cooperative transmission strategy, gives an optimal node selection algorithm using convex optimization theory. Theoretical analysis and simulation indicate that this scheme can give good performance of maximizing the channel capacity through optimal node selection.
18813613
Efficient Training of RBF Networks Via the BYY Automated Model Selection Learning Algorithms
Radial basis function (RBF) networks of Gaussian activation functions have been widely used in many applications due to its simplicity, robustness, good approximation and generalization ability, etc.. However, the training of such a RBF network is still a rather difficult task in the general case and the main crucial problem is how to select the number and locations of the hidden units appropriately. In this paper, we utilize a new kind of Bayesian Ying-Yang (BYY) automated model selection (AMS) learning algorithm to select the appropriate number and initial locations of the hidden units or Gaussians automatically for an input data set. It is demonstrated well by the experiments that this BYY-AMS training method is quite efficient and considerably outperforms the typical existing training methods on the training of RBF networks for both clustering analysis and nonlinear time series prediction.
14438515
Asymptotic convergence properties of the EM algorithm with respect to the overlap in the mixture
The EM algorithm is generally considered as a linearly convergent algorithm. However, many empirical results show that it can converge significantly faster than those gradient based first-order iterative algorithms, especially when the overlap of densities in a mixture is small. This paper explores this issue theoretically on mixtures of densities from a class of exponential families. We have proved that as an average overlap measure of densities in the mixture tends to zero, the asymptotic convergence rate of the EM algorithm locally around the true solution is a higher order infinitesimal than a positive order power of this overlap measure. Thus, the large sample local convergence rate for the EM algorithm tends to be asymptotically superlinear when the overlap of densities in the mixture tends to zero. Moreover, this result has been detailed on Gaussian mixtures.
6394511
The capacity of time-delay recurrent neural network for storing spatio-temporal sequences
We investigate the capacity of a type of discrete-time recurrent neural network, called time-delay recurrent neural network, for storing spatio-temporal sequences. By introducing the order of a spatio-temporal sequence, the match law between a time-delay recurrent neural network and a spatio-temporal sequence has been established. It has been proved that the full order time-delay recurrent neural network of l-step feedback is able to learn and memorize (or store) any bipolar (or binary) spatio-temporal sequence of the order k if k≤l, and that the asymptotic memory capacity of the first-order time-delay recurrent neural network of one-step feedback is not less than C1(n)=n+1, where n is the number of processing neurons in the network. Moreover, we substantiate the theoretical results by simulation experiments.
12498019
An Information Criterion for Informative Gene Selection
It is important in bioinformatics research and applications to select or discover informative genes of a tumor from microarray data. However, most of the existing methods are based on models which assume that the gene expressions are normal distributed, which is often violated in practice. In this paper, we propose an information criterion for informative gene selection by ranking the genes with the Kullback-Leiber discrimination information of two probability distributions of the expression levels on the tumor and normal (or another type of tumor) samples. We use support vector machine (SVM) to construct the tumor diagnosis system using certain top informative genes. The experiments on two well-known data sets (colon data and leukemia data) show that the information criterion can make the tumor diagnosis system reach 94.4% and 100% correctness rate of diagnosis on these two datasets, respectively.