Branch-and-Bound Placement for Building Block Layout

This paper proposes a placement technique based on the branch-and-bound method for the block placement problem in building block layout. In contrast to a traditional method of finding an approximate solution by a heuristic approach, the proposed method seeks a solution from all possible placements. To find the solution efficiently, the branch-and-bound operation suited to the placement problem is devised. The proposed method positively considers the constraints imposed on routing length and placement configuration since they could be utilized for restricting the solution space. When the constraints are stronger, the solution space is more restricted, which helps to complete the search of the solution in a short time. By an experimental investigation concerning the number of blocks that can be handled at a time, it is seen that almost six blocks can be handled if there is no constraint. When the number of blocks exceeds this limit, the circuit is decomposed in a hierarchical way and the branch-and-bound placement is applied to each subproblem until the layout of the whole circuit is determined. The proposed placement method is applied to the standard benchmark circuit for building block layout, and it is seen that the result by the proposed method is better than or very close to the best result reported so far.