TY - GEN

T1 - Lower bounds on the complexity of simplex range reporting on a pointer machine

AU - Chazelle, Bernard

AU - Rosenberg, Burton

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1992.

PY - 1992

Y1 - 1992

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.

AB - 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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U2 - 10.1007/3-540-55719-9_95

DO - 10.1007/3-540-55719-9_95

M3 - Conference contribution

AN - SCOPUS:84976668911

SN - 9783540557197

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 439

EP - 449

BT - Automata, Languages and Programming - 19th International Colloquium, Proceedings

A2 - Kuich, Werner

PB - Springer Verlag

T2 - 19th International Colloquium on Automata, Languages, and Programming, ICALP 1992

Y2 - 13 July 1992 through 17 July 1992

ER -