Fast Evaluation of Bounded Slice-Line Grid

Bounded Slice-line Grid (BSG). is an elegant representation of block placement, because it is very intuitionistic and has the advantage of handling various placement constraints. However, BSG has attracted little attention because its evaluation is very time-consuming. This paper proposes a simple algorithm independent of the BSG size to evaluate the BSG representation in O(nloglogn) time, where n is the number of blocks. In the algorithm, the BSG-rooms are assigned with integral coordinates firstly, and then a linear sorting algorithm is applied on the BSG-rooms where blocks are assigned to compute two block sequences, from which the block placement can be obtained in O(n log log n) time. As a consequence, the evaluation of the BSG is completed in O(n log log n) time, where n is the number of blocks. The proposed algorithm is much faster than the previous graph-based O(n2) algorithm. The experimental results demonstrate the efficiency of the algorithm.