Optimal paths in graphs with stochastic or multidimensional weights
Communications of the ACM
A graph based algorithm for optimal buffer insertion under accurate delay models
Proceedings of the conference on Design, automation and test in Europe
A general probabilistic framework for worst case timing analysis
Proceedings of the 39th annual Design Automation Conference
Introduction to Algorithms
Parameter variations and impact on circuits and microarchitecture
Proceedings of the 40th annual Design Automation Conference
First-order incremental block-based statistical timing analysis
Proceedings of the 41st annual Design Automation Conference
Variational delay metrics for interconnect timing analysis
Proceedings of the 41st annual Design Automation Conference
Block-based Static Timing Analysis with Uncertainty
Proceedings of the 2003 IEEE/ACM international conference on Computer-aided design
Statistical Timing Analysis Considering Spatial Correlations using a Single Pert-Like Traversal
Proceedings of the 2003 IEEE/ACM international conference on Computer-aided design
Statistical static timing analysis: how simple can we get?
Proceedings of the 42nd annual Design Automation Conference
A novel criticality computation method in statistical timing analysis
Proceedings of the conference on Design, automation and test in Europe
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Graph algorithms are widely used in VLSI CAD. Traditional graph algorithms can handle graphs with deterministic edge weights. As VLSI technology continues to scale into nanometer designs, we need to use probability distributions for edge weights in order to model uncertainty due to parameter variations. In this paper, we consider the statistical shortest path (SSP) problem. Given a graph G, the edge weights of G are random variables. For each path P in G, let LP be its length, which is the sum of all edge weights on P. Clearly LP is a random variable and we let μP and σ2P be its mean and variance, respectively. In the SSP problem, our goal is to find a path P connecting two given vertices to minimize the cost function μP + Φ (σ2P) where Φ is an arbitrary function. (For example, if Φ (x) = 3√x, the cost function is μ + 3σP.) To minimize uncertainty in the final result, it is meaningful to look for paths with bounded variance, i.e., σ2P ≤ B for a given fixed bound B. In this paper, we present an exact algorithm to solve the SSP problem in O(B(V + E)) time where V and E are the numbers of vertices and edges, respectively, in G. Our algorithm is superior to previous algorithms for SSP problem because we can handle: 1) general graphs (unlike previous works applicable only to directed acyclic graphs), 2) arbitrary edge-weight distributions (unlike previous algorithms designed only for specific distributions such as Gaussian), and 3) general cost function (none of the previous algorithms can even handle the cost function μP + 3σP Finally, we discuss applications of the SSP problem to maze routing, buffer insertions, and timing analysis under parameter variations.