Construction of All Rectilinear Steiner Minimum Trees on the Hanan Grid and Its Applications to VLSI Design

A rectilinear Steiner minimum tree (RSMT) is a rectilinear Steiner tree connecting a given set of pins with the shortest wirelength. RSMT construction is one of the most frequently used algorithms in the physical design automation, including floorplanning, placement, routing, and interconnect estimation and optimization. Thus, efficient algorithms to construct RSMTs have been developed for many years in academia and industry. Unfortunately, RSMT construction is an NP-hard problem, so even a fast RSMT construction algorithm, such as GeoSteiner is too slow to use in physical design automation tools. FLUTE, a fast lookup-table-based RSMT construction algorithm, builds and uses a routing topology database to quickly construct RSMTs. In this paper, we present an algorithm to build a database (ARSMT DB) to construct all RSMTs on the Hanan grid for a given set of pins. ARSMT DB constructs all RSMTs in almost no time, so numerous applications could use it for various purposes. We apply the ARSMT DB to two applications, timing-driven RSMT construction and congestion-aware global routing, and show that the ARSMT DB can help reduce source-to-critical-sink lengths, source-to-critical-sink delays, and routing congestion significantly. Since the size of the original ARSMT DB is too large, we present techniques to reduce the database size.