The cell probe complexity of dynamic data structures
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Lower bounds for orthogonal range searching: I. The reporting case
Journal of the ACM (JACM)
Lower bounds for off-line range searching
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Simplex range reporting on a pointer machine
Computational Geometry: Theory and Applications
A Spectral Approach to Lower Bounds with Applications to Geometric Searching
SIAM Journal on Computing
The Complexity of Maintaining an Array and Computing Its Partial Sums
Journal of the ACM (JACM)
A trace bound for the hereditary discrepancy
Proceedings of the sixteenth annual symposium on Computational geometry
Lower bounds for intersection searching and fractional cascading in higher dimension
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Logarithmic Lower Bounds in the Cell-Probe Model
SIAM Journal on Computing
Lower bounds for 2-dimensional range counting
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Tradeoffs in Approximate Range Searching Made Simpler
SIBGRAPI '08 Proceedings of the 2008 XXI Brazilian Symposium on Computer Graphics and Image Processing
Higher Lower Bounds for Near-Neighbor and Further Rich Problems
SIAM Journal on Computing
Proceedings of the twenty-sixth annual symposium on Computational geometry
On Range Searching in the Group Model and Combinatorial Discrepancy
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Higher-dimensional orthogonal range reporting and rectangle stabbing in the pointer machine model
Proceedings of the twenty-eighth annual symposium on Computational geometry
Improved pointer machine and I/O lower bounds for simplex range reporting and related problems
Proceedings of the twenty-eighth annual symposium on Computational geometry
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In this paper we present a number of improved lower bounds for range searching in the pointer machine and the group model. In the pointer machine, we prove lower bounds for the approximate simplex range reporting problem. In approximate simplex range reporting, points that lie within a distance of ε ⋅ Diam(s) from the border of a query simplex s, are free to be included or excluded from the output, where ε ≥ 0 is an input parameter to the range searching problem. We prove our lower bounds by constructing a hard input set and query set, and then invoking Chazelle and Rosenberg's [CGTA'96] general theorem on the complexity of navigation in the pointer machine. For the group model, we show that input sets and query sets that are hard for range reporting in the pointer machine (i.e. by Chazelle and Rosenberg's theorem), are also hard for dynamic range searching in the group model. This theorem allows us to reuse decades of research on range reporting lower bounds to immediately obtain a range of new group model lower bounds. Amongst others, this includes an improved lower bound for the fundamental problem of dynamic d-dimensional orthogonal range searching, stating that tqtu = Ω((lg n/lg lg n)d-1). Here tq denotes the query time and tu the update time of the data structure. This is an improvement of a lg1-δn factor over the recent lower bound of Larsen [FOCS'11], where δ0 is a small constant depending on the dimension.