Mapped regular pavings

Jennifer Harlow, Raazesh Sainudiin, Warwick Tucker

Research output: Contribution to journalArticleResearchpeer-review

6 Citations (Scopus)


A regular paving is a finite succession of bisections that partition a root box x in ℝd 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.

Original languageEnglish
Pages (from-to)252-282
Number of pages31
JournalReliable Computing
Publication statusPublished - 27 Nov 2012
Externally publishedYes


  • Finite rooted binary trees
  • Inclusion algebra
  • Tree arithmetic

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