Branch-and-bound placement for building block layout

We present a branch-and-bound placement technique for building block layout that effectively searches for an optimal placement in the whole solution space. We first describe a block placement problem and its solution space. Then we explain branching and bounding operations designed for the placement problem. Constraints on critical nets and/or the shape of a resulting chip can be taken into account in the search process. Experiments reveals that the number of blocks the method can manage is around six if the whole solution space is explored. For a problem which contains more blocks than the limit, we decompose the problem hierarchically and apply the method to each subproblem. The results for standard benchmark examples and a comparison with those of other systems are given to demonstrate the performance of the method.