On the Array Embeddings and Layouts of Quadtrees and Pyramids

Quadtree and pyramid structures have attracted considerable attention in recent years. They are increasingly being applied to the fields of digital image and signal processing. As a result, the efficient embedding of these structures in VLSI arrays has become an important research topic. In this paper, we propose three schemes to embed either quadtrees or pyramids in a rectangular, hexagonal, or octagonal mesh, respectively, with three different node shapes for VLSI layout. Our analyses show that the best achievable node utilization is 67% when embedding either structure in an octagonal mesh. This result outperforms the best utilization recorded in literature by 25%. Our study also indicates that the octagonal node gives the most favorable compromise between high area utilization desired and routing space required among the processing nodes.