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 δ+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(n d(1-δ)-ε), for any fixed ε > 0. This lower bound is tight within a factor of 2 ε.
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© 1992 Springer-Verlag Berlin Heidelberg
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Chazelle, B., Rosenberg, B. (1992). Lower bounds on the complexity of simplex range reporting on a pointer machine. In: Kuich, W. (eds) Automata, Languages and Programming. ICALP 1992. Lecture Notes in Computer Science, vol 623. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55719-9_95
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DOI: https://doi.org/10.1007/3-540-55719-9_95
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