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In this paper we describe the quad-CIF tree data structure and its application to hierarchical on-line computer-aided design algorithms. The main idea is to overlay a tree of coordinates on top of the hierarchical representation of an integrated circuit. The coordinate tree enables one to find quickly the set of all objects that intersect a given window. We outline how one can use the data structure in order to implement hierarchical, on-line design rule checking and node extraction. We also describe some applications to plotting.