An efficient decoding method of sequence-pair

The sequence-pair was proposed as a representation method of block placement to determine the densest possible placement of rectangular modules in VLSI layout design. In this paper, we propose a method of obtaining packing via the Q-sequence (representation of rectangular dissection) in O(n+k) time from a given sequence-pair of n rectangles with k subsequences called adjacent crosses, given the position of adjacent crosses and the insertion order of dummy modules into adjacent crosses. We confirm theoretically and experimentally that the proposed method decodes a sequence-pair in O(n+k) time. It was proved that arbitrary packing can be represented by a sequence-pair, keeping the value of k not more than n-3. Therefore, we can determine packing from a sequence-pair with k of O(n) in linear time using the proposed method and the conventional method.