Mapped regular pavings (2012)
Type of ContentConference Contributions - Other
PublisherUniversity of Canterbury. Computer Science and Software Engineering
University of Canterbury. Mathematics and Statistics
AuthorsHarlow, Jennifer, Sainudiin, R., Tucker, W.show all
A regular paving is a finite succession of bisections that partition a root box x in R^d into subboxes using a binary tree-based data structure. We extend regular pavings to mapped regular pavings which map sub-boxes in a regular paving of x to elements in some set Y. Arithmetic operations defined on Y can be extended point-wise over x and carried out in a computationally efficient manner using Y-mapped regular pavings of x. The efficiency of this arithmetic is due to recursive algorithms on the algebraic structure of finite rooted binary trees that are closed under union operations. Our arithmetic has many applications in function approximation using tree based inclusion algebras and statistical set-processing.
CitationHarlow, J., Sainudiin, R., Tucker, W. (2012) Mapped regular pavings. Uppsala University, Sweden: Intervals Pavings and Applications (IPA), 15-17 Oct 2012.
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