Using red-black interval trees in device-level analog placement with symmetry constraints

The traditional way of approaching device-level placement problems for analog layout is to explore a huge search space of absolute placement representations, where cells are allowed to illegally overlap during their moves. This paper presents a novel exploration technique for analog placement, operating on the set of tree representations of the layout, where the typical presence of an arbitrary number of symmetry groups of devices is directly taken into account during the search of the solution space. The efficiency of the novel approach is due to the use of red-black interval trees (T.H. Cormen et al, Introduction to Algorithms, McGraw-Hill, 1990), data structures employed to support operations on dynamic sets of intervals.