On handling arbitrary rectilinear shape constraint

Abstract

Non-rectangular (rectilinear) shape occurs very often in deep submicron floorplanning. Most previous algorithms are designed to handle only convex rectilinear blocks. However, handling concave rectilinear shape is necessary since a simple "U" shape is concave. A few works could address concave rectilinear block explicitly. In [2], a necessary and sufficient condition of feasible sequence pair is proposed for arbitrary rectilinear shape in terms of constraint graph. However, no constraint is imposed on sequence pair representation itself. The search for feasible sequence pair mainly depends on the simulated annealing, which implies unnecessary inefficiency. In many cases, it takes very long time or even is unable to find the feasible placement. Furthermore, it takes O ¡ n 3 ¢ runtime to evaluate each sequence pair, which leaves much space for improvement. In this paper, we propose a new method to handle arbitrary rectilinear shape constraint based on sequence pair representation. We explore the topological property of feasible sequence pair, and use it to eliminate lots of infeasible sequence pairs, which implies speeding up the convergence of simulated annealing process. The evaluation of a sequence pair is based on longest common subsequence computation, and achieves significantly faster runtime (O ¡ mn log log n ¢ time where m is the number of rectilinear-shape constraints, n is the number of rectangular blocks/subblocks). The algorithm can handle fixed-frame floorplanning and min-area floorplanning as well.

A fast algorithm for rectilinear block packing based on selected sequence-pair

“…Also, we propose an efficient algorithm to obtain a rectilinear block packing in Oððp þ 1ÞnÞ time 2 keeping all the constraints imposed by a given SSP. Time complexity of our method is close to that of [14] but p is the number of rectilinear blocks excluding rectangles. 3 So, obviously ppm because m is more than the number of rectilinear blocks as mentioned before.…”

“…3 So, obviously ppm because m is more than the number of rectilinear blocks as mentioned before. Hence, when complex rectilinear blocks are packed, our method is faster than the method of [14]. The proposed method requires only OðnÞ time if p is constant.…”

“…Another method to obtain a rectilinear block packing in Oðmn log log nÞ time was proposed in [14], 1 where m is not the number of rectilinear blocks but the number of sets of H/V-sequential sub-blocks. In [14], ''a rectilinear block is said to be H-sequential (V-sequential) if no vertical (horizontal) line cuts the block into more than two parts''.…”

“…In [14], ''a rectilinear block is said to be H-sequential (V-sequential) if no vertical (horizontal) line cuts the block into more than two parts''. The blocks partitioned from a H-sequential (V-sequential) rectilinear block is said to be H-sequential (V-sequential) sub-blocks.…”

Floorplan Design and Yield Enhancement of 3-D Integrated Circuits

“…These rectilinear shapes are usually handled by partitioning them into small rectangular blocks, and imposing rectilinear constraints on the floorplan representation such that the partitioned parts of a rectilinear block preserve its original rectilinear shape. The partition based rectilinear shape constraints have been reported on several floorplan representations such as on SP [68], [100], [116], BSG [114][115], 0-tree [11 7], CBL [118], B* tree [119], and TCG [120]. Although the rectilinear block packing can be done using any of these representations, it is easy to satisfy these constraints on sequence pair for which a fast module packing algorithm satisfying these constraints has been proposed in [100].…”