Refactoring of Timing Graphs and Its Use in Capturing Topological Correlation in SSTA

Reconvergent paths in circuits have been a nuisance in various computer-aided design (CAD) algorithms, but no elegant solution to deal with them has been found yet. In statistical static timing analysis (SSTA), they cause difficulty in capturing topological correlation. This paper presents a technique that in arbitrary block-based SSTA reduces the error caused by ignoring topological correlation. We interpret a timing graph as an algebraic expression made up of addition and maximum operators. We define the division operation on the expression and propose algorithms that modify factors in the expression without expansion. As a result, the algorithms produce an expression to derive the latest arrival time with better accuracy in SSTA. Existing techniques handling reconvergent fanouts usually use dependency lists, requiring quadratic space complexity. Instead, the proposed technique has linear space complexity by using a new directed acyclic graph search algorithm. Our results show that it outperforms an existing technique in speed and memory usage with comparable accuracy. More important, the proposed technique is not limited to SSTA and is potentially applicable to various issues due to reconvergent paths in timing-related CAD algorithms.