Bisection trees and half-quad trees: Memory and time efficient data structures for VLSI layout editors

Abstract

In this paper, we present two new tree structures, bisection trees and half-quad trees that can be used as data structures for storing VLSI layouts. The bisection tree is based on the structure of a 2-d tree and the half-quad tree is constructed based on the bisection tree and the quad tree. These two trees perform as good as of 4-d tree in terms a speed but require less memory. Specifically, our experimental results show that, for region queries, the bisection tree has approximately the same nodes visited as the 4-d tree. In addition, the bisection tree requires less memory space and simpler procedures. For the half-quad tree, it is shown that it approximately 50% memory of that used by the 4-d tree which is approximately the same as the memory used by the quad tree. In addition, the half-quad tree achieves a much better speed than the quad tree.