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 a subset 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, data structures employed to support operations on dynamic sets of intervals.

Layout design for analog circuits has historically been a time consuming, error-prone, manual task. Its complexity results not so much from the number of devices, as from the complex interactions among devices or with the operating environment, and also from continuous-valued performance specifications. This paper addresses the problem of device-level placement for analog layout in a non-traditional way. Different from the classic approaches--exploring a huge search space with a combinatorial optimization technique, where the cells are represented by means of absolute coordinates, being allowed to illegally overlap during their moves in the chip plane--this paper advocates the use of non-slicing topological representations, like (symmetric-feasible) sequence-pairs, ordered- and binary- trees. Extensive tests, processing industrial analog designs, have shown that using skillfully the symmetry constraints (very typical to analog circuits) to remodel the solution space of the encoding systems, the topological representation techniques can achieve a better computation speed than the traditional approaches, while obtaining a similar high quality of the designs.