Statistical static timing analysis via modern optimization lens: I. Histogram-based approach

TL;DR

This paper introduces novel optimization-based formulations for statistical static timing analysis, employing binary-integer programming and geometric programming with histogram approximations to improve scalability and understanding.

Contribution

It presents the first known formulations of SSTA as binary-integer and geometric programming problems, advancing the mathematical modeling of timing analysis.

Findings

New formulations enable better scalability.

Histogram approximation simplifies complex distributions.

Approaches are discussed for potential generalizations.

Abstract

Statistical static timing analysis (SSTA) is studied from the point of view of mathematical optimization. We present two formulations of the problem of finding the critical path delay distribution that were not known before: (i) a formulation of the SSTA problem using Binary--Integer Programming and (ii) a practical formulation using Geometric Programming. For simplicity, we use histogram approximation of the distributions. Scalability of the approaches is studied and possible generalizations are discussed.