Lower Bounds on the Complexity of Simplex Range Reporting on a Pointer Machine

Abstract Bernard Chazelle Department of Computer Science Princeton University Burton Rosenberg Department of Mathematics and Computer Science Dartmouth College 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 +r), where r is the number of points to be reported and is an arbitrary fixed real. We prove that any such data structure of that form must occupy storage (nd(1-)), for any fixed > 0. This lower bound is tight within a factor of n .

• Type: Conference
• Year: 1992
• Where: ICALP
• Authors: Bernard Chazelle, Burton Rosenberg
• Keywords: Arbitrary Simplex Q, Computer Science, ICALP 1992, Lower Bound, Programming Languages