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

Bernard Chazelle; Burton Rosenberg

doi:10.1007/3-540-55719-9_95

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

Bernard Chazelle, Burton Rosenberg

Research output: Chapter in Book/Report/Conference proceeding › Conference 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(n^ε+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(n^d(^l-δ)-e), for any fixed epsi > 0. This lower bound is tight within a factor of n^ε.

Original language	English (US)
Title of host publication	Automata, Languages and Programming - 19th International Colloquium, Proceedings
Editors	Werner Kuich
Publisher	Springer Verlag
Pages	439-449
Number of pages	11
ISBN (Print)	9783540557197
DOIs	https://doi.org/10.1007/3-540-55719-9_95
State	Published - 1992
Externally published	Yes
Event	19th International Colloquium on Automata, Languages, and Programming, ICALP 1992 - Wien, Austria Duration: Jul 13 1992 → Jul 17 1992

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	623 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	19th International Colloquium on Automata, Languages, and Programming, ICALP 1992
Country/Territory	Austria
City	Wien
Period	7/13/92 → 7/17/92

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/3-540-55719-9_95

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

Chazelle, Bernard ; Rosenberg, Burton. / Lower bounds on the complexity of simplex range reporting on a pointer machine. Automata, Languages and Programming - 19th International Colloquium, Proceedings. editor / Werner Kuich. Springer Verlag, 1992. pp. 439-449 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 623 LNCS, Springer Verlag, pp. 439-449, 19th International Colloquium on Automata, Languages, and Programming, ICALP 1992, Wien, Austria, 7/13/92. https://doi.org/10.1007/3-540-55719-9_95

Lower bounds on the complexity of simplex range reporting on a pointer machine. / Chazelle, Bernard; Rosenberg, Burton.
Automata, Languages and Programming - 19th International Colloquium, Proceedings. ed. / Werner Kuich. Springer Verlag, 1992. p. 439-449 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 623 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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N2 - 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.

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

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

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