Lower bounds on the complexity of simplex range reporting on a pointer machine

Bernard Chazelle, Burton Rosenberg

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 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(nε+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 Π(nd(l-δ)-e), for any fixed epsi > 0. This lower bound is tight within a factor of nε.

Original languageEnglish (US)
Title of host publicationAutomata, Languages and Programming - 19th International Colloquium, Proceedings
EditorsWerner Kuich
PublisherSpringer Verlag
Pages439-449
Number of pages11
ISBN (Print)9783540557197
DOIs
StatePublished - Jan 1 1992
Event19th International Colloquium on Automata, Languages, and Programming, ICALP 1992 - Wien, Austria
Duration: Jul 13 1992Jul 17 1992

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume623 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other19th International Colloquium on Automata, Languages, and Programming, ICALP 1992
CountryAustria
CityWien
Period7/13/927/17/92

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Chazelle, B., & Rosenberg, B. (1992). Lower bounds on the complexity of simplex range reporting on a pointer machine. In W. Kuich (Ed.), Automata, Languages and Programming - 19th International Colloquium, Proceedings (pp. 439-449). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 623 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-55719-9_95