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Abstract: Majority of practical multivariate statistical analysis and optimizations model interdependence among random variables in terms of the linear correlation. Though linear correlation is simple to use and evaluate, in several cases non-linear dependence between random variables may be too strong to ignore. In this paper, we propose polynomial correlation coefficients as simple measure of multi-variable non-linear dependence and show that the need for modeling non-linear dependence strongly depends on the end function that is to be evaluated from the random variables. Then, we calculate the errors in estimation resulting from assuming independence of components generated by linear de-correlation techniques, such as PCA and ICA. The experimental results show that the error predicted by our method is within 1% error compared to the real simulation of statistical timing and leakage analysis. In order to deal with non-linear dependence, we further develop a target-function-driven component analysis algorithm (FCA) to minimize the error caused by ignoring high order dependence. We apply FCA to statistical leakage power analysis and SRAM cell noise margin variation analysis. Experimental results show that the proposed FCA method is more accurate compared to the traditional PCA or ICA. [Copyright &y& Elsevier]

With the increase of the complexity of circuits, fast estimation can provide some vital information for optimal layout decisions. Fast congestion prediction plays an important role in the physical layout of VLSI design. In this paper, we present a probabilistic estimation approach with via minimization constraints. Our model is more realistic than previous models. It has more flexibility for wires to have more usage area to bypass congested regions and blockages. The experiment on routing benchmarks demonstrates the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

Interconnect planning is an important issue in VLSI designs. Routing congestion is an important problem during placement. This paper presents a novel approach to estimating the routing congestion on the hexagonal model with bounded-length detours. It is the first probabilistic estimation work on hexagonal topologies. A combinatorial estimation algorithm is presented. The experimental results demonstrate the effectiveness of the method. [ABSTRACT FROM AUTHOR]

Abstract: Congestion estimation plays an important role in the physical layout of VLSI design. This paper presents a new probabilistic estimation model that improves the previous estimators by relaxing the constraint on detours in a route. The model is more general and realistic for it gives the flexibility for the wires to have wider usage area to bypass the congestion regions and blockages. Given a routing grid and a set of nets to be routed, the model predicts the routing density on each edge of the grid. The routing density provides direct congestion estimation. We compare our estimation results to the actual routing results. Experimental results show the effectiveness of our estimator. [Copyright &y& Elsevier]