A Probabilistic Approach to Buffer Insertion

This work presents a formal probabilistic approach for solving optimizationproblems in design automation. Prediction accuracy isvery low especially at high levels of design flow. This can be attributedmainly to unawareness of low level layout information andvariability in fabrication process. Hence a traditional deterministicdesign automation approach where each cost function is representedas a fixed value becomes obsolete. A new approach is gainingattention in which the cost functions are representedas probability distributions and the optimization criteriais probabilistic too. This design optimization philosophy is demonstratedthrough the classic buffer insertion problem. Formally,we capture wirelengths as probability distributions (as compared tothe traditional approach which considers wirelength as fixed values)and present several strategies for optimizing the probabilisticcriteria. During the course of this work many problems are provedto be NP-Complete. Comparisons are made with the Van-Ginneken"optimal under fixed wire-length" algorithm. Results show that theVan-Ginneken approach generated delay distributions at the root ofthe fanout wiring tree which had large probability (0.91 in the worstcase and 0.55 on average) of violating the delay constraint. Ouralgorithms could achieve 100% probability of satisfying the delayconstraint with similar buffer penalty. Although this work considerswirelength prediction inaccuracies, our probabilistic strategy couldbe extended trivially to consider fabrication variability in wire parasitics.