Topics in parallel integer optimization

Ph.D.Martin Savelsberg

Congestion analysis for global routing via integer programming

Abstract — This work presents a fast and flexible framework for congestion analysis at the global routing stage. It captures various factors that contribute to congestion in modern designs. The framework is a practical realization of a proposed parameterized integer programming formulation. The formulation minimizes overflow inside a set of regions covering the layout which is defined by an input resolution parameter. A resolution lower than the global routing grid-graph creates regions that are larger in size than the global-cells. The maximum resolution case simplifies the formulation to minimizing the total overflow which has been traditionally used as a metric to evaluate routability. A novel contribution of this work is to demonstrate that for a small analysis time budget, regional minimization of overflow with a lower resolution allows a more accurate identification of the routing congestion hotspot locations, compared to minimizing the total overflow. It allows generating a more accurate congestion heatmap. The other contributions include several new ideas for a practical realization of the formulation for industrysized benchmark instances some of which are also improvements to existing global routing procedures. This work also describes coalesCgrip, a simpler variation of our framework which was used to evaluate the ISPD 2011 contest. I

A Parallel Integer Programming Approach to Global Routing

We propose a parallel global routing algorithm that concurrently processes routing subproblems corresponding to rectangular subregions covering the chip area. The algorithm uses at it core an existing integer programming (IP) formulation—both for routing each subproblem and for connecting them. Concurrent processing of the routing subproblems is desirable for effective parallelization. However, achieving no (or low) overflow global routing solutions without strong, coordinated algorithmic control is difficult. Our algorithm addresses this challenge via a patching phase that uses IP to connect partial routing solutions. Patching provides feedback to each routing subproblem in order to avoid overflow, later when attempting to connect them. The end result is a flexible and highly scalable distributed algorithm for global routing. The method is able to accept as input target runtimes for its various phases and produce high-quality solution within these limits. Computational results show that for a target runtime of 75 minutes, running on a computational grid of few hundred CPUs with 2GB memory, the algorithm generates higher quality solutions than competing methods in the open literature

Contents

1.1 LP/NLP-based Branch and Bound...................... 4 1.2 Implementation within the MINTO Framework...............