Evaluating a bounded slice-line grid assignment in O(nlogn) time

Bounded Slice-line Grid (BSG) is an elegant representation of block placement/floorplan. All block placement algorithms based on a bounded slice-line grid make use of simulated annealing or solution space smoothing where the generation and evaluation of a large number of BSG assignments is required. Therefore, a fast algorithm is needed to evaluate the BSG assignments. We present a very simple and efficient O(nlogn) algorithm to evaluate the BSG assignments. Implementation of our algorithm is significantly faster than the original O(p×q) graph-based algorithm, where p×q is BSG size. The graph-based algorithm and our algorithm are embedded in a space smoothing search procedure. Experimental results demonstrate the efficiency of our algorithm.