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Data & Maps
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The Combinatorial Complexity of Polygon Overlay
The Combinatorial Complexity of Polygon Overlay
RR89-02
Abstract
The number of elementary connected regions arising from polygon overlay of two or more map layers is an important value to have in planning for data storage and in making processing time estimates for overlay applications. That number may be computed directly from the line graphs of the two (or more) layers and from the intersection graph(s) of those line graphs. A formula for that computation is derived using tools of algebraic and combinatorial topology which relate the connectivity of a union of sets to the connectivity of the sets themselves and their intersection.
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WORKING PAPER
Statistical Research Reports and Studies
Page Last Revised - October 28, 2021
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