Nearly Balanced Quad List Quad Tree -A Data Structure for VLSI Layout Systems

Abstract

In the past ten years, many researchers have focused attention on developing better data structures for storing graphical information. Among the proposed data structures, the quad tree data structure provides a good way to organize objects on a 2-D plane. Region searches proceed at logarithmic speeds a desirable characteristic, but no previously proposed VLSI quad tree data structure distributed objects to subdivide the spatial area. This has been a major drawback for operations such as tree searching and window query. In this paper, we present a new division method to reconstruct those quad trees including the multiple storage quad tree (MSQT) and the quad list quad tree (QLQT) into nearly balanced quad tree data structures. Nearly balanced quad trees based on our new spatial division method are constructed by dynamically translating unbalanced multiple storage quad trees or unbalanced quad list quad trees into balanced structures. All benefits of the original quad tree data structures are completely retained. In addition, this method is simple and balanced quad trees memory require less than the original quad trees. Experimental results illustrate that the improvement in region queries of the presented nearly balanced quad trees to both of the QLQT and the MSQT is better than the improvement of the QLQT to the MSQT.