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Mapped regular pavings
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2012 (English)In: Reliable Computing, ISSN 1385-3139, E-ISSN 1573-1340, Vol. 16, 252-282 p.Article in journal (Refereed) Published
Abstract [en]

A regular paving is a finite succession of bisections that partition a root box x in ℝ d into sub-boxes 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.

Place, publisher, year, edition, pages
2012. Vol. 16, 252-282 p.
Keyword [en]
Finite rooted binary trees, Inclusion algebra, Tree arithmetic
National Category
URN: urn:nbn:se:uu:diva-188127OAI: oai:DiVA.org:uu-188127DiVA: diva2:576634
Available from: 2012-12-13 Created: 2012-12-12 Last updated: 2012-12-13Bibliographically approved

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