Simplex range reporting on a pointer machine

Bernard Chazelle, Burton Rosenberg

Research output: Contribution to journalArticle

22 Scopus citations

Abstract

We give a lower bound on the following problem, known as simplex range reporting: Given a collection P of n points in d-space and an arbitrary simplex q, find all the points in P ∩ q. It is understood that P is fixed and can be preprocessed ahead of time, while q is a query that must be answered on-line. We consider data structures for this problem that can be modeled on a pointer machine and whose query time is bounded by O(nδ + r), where r is the number of points to be reported and δ is an arbitrary fixed real. We prove that any such data structure of that form must occupy storage Ω(nd(1-δ)-ε), for any fixed ε > 0. This lower bound is tight within a factor of nε.

Original languageEnglish (US)
Pages (from-to)237-247
Number of pages11
JournalComputational Geometry: Theory and Applications
Volume5
Issue number5
DOIs
StatePublished - Jan 1996

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics

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