An optimal two-dimensional orthogonal range search algorithm in VLSI, design automation

It is well known that an optimal algorithm for logarithm query time and linear storage for two dimensional orthogonal range searches is nonexistent except for very few cases in which certain computational models have been assumed. A new algorithm called sliding kd tree is presented in this article where the length of the query box is fixed in any direction. The new algorithm is optimal in handling two-dimensional problems, and can be applied to VLSI Design Automations presented to show the performance of the SKD algorithm.