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How hard is half-space range searching?
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1007/3-540-55719-9_95openalex-snapshot
Lower bounds on the complexity of simplex range reporting on a pointer machine
inferredcites →https://doi.org/10.1007/978-3-642-69900-9openalex-snapshot
Data Structures and Algorithms 3
inferredcites →https://doi.org/10.1007/978-3-642-97881-4openalex-snapshot
Geometric Algorithms and Combinatorial Optimization
inferredcites →https://doi.org/10.1007/bf01238645openalex-snapshot
On the mean value of the volume of a random polytope in a convex set
inferredcites →https://doi.org/10.1007/bf01758854openalex-snapshot
Quasi-optimal upper bounds for simplex range searching and new zone theorems
inferredcites →https://doi.org/10.1007/bf02187740openalex-snapshot
Applications of random sampling in computational geometry, II
inferredcites →https://doi.org/10.1007/bf02187743openalex-snapshot
Quasi-optimal range searching in spaces of finite VC-dimension
inferredcites →https://doi.org/10.1007/bf02189304openalex-snapshot
Applications of a new space-partitioning technique
inferredcites →https://doi.org/10.1016/0020-0190(86)90088-8openalex-snapshot
Halfplanar range search in linear space and O(n0.695) query time
inferredcites →https://doi.org/10.1016/0304-3975(81)90099-2openalex-snapshot
Inherent complexity trade-offs for range query problems
inferredcites →https://doi.org/10.1016/0925-7721(92)90006-eopenalex-snapshot
Reporting points in halfspaces
inferredcites →https://doi.org/10.1016/s0019-9958(84)80040-6openalex-snapshot
Geometric retrieval problems
inferredcites →https://doi.org/10.1017/cbo9780511617331openalex-snapshot
Integral Geometry and Geometric Probability
inferredcites →https://doi.org/10.1017/cbo9781107325630.013openalex-snapshot
ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS
inferredcites →https://doi.org/10.1090/s0894-0347-1989-1001852-0openalex-snapshot
Lower Bounds on the Complexity of Polytope Range Searching
inferredcites →https://doi.org/10.1109/sfcs.1991.185370openalex-snapshot
Reporting points in halfspaces
inferredcites →https://doi.org/10.1112/s0025579300002655openalex-snapshot
The directions of the line segments and of the r ‐dimensional balls on the boundary of a convex body in Euclidean space
inferredcites →https://doi.org/10.1112/s0025579300015266openalex-snapshot
Convex bodies, economic cap coverings, random polytopes
inferredcites →https://doi.org/10.1137/0210001openalex-snapshot
Lower Bounds on the Complexity of Some Optimal Data Structures
inferredcites →https://doi.org/10.1137/0214022openalex-snapshot
On the Complexity of Maintaining Partial Sums
inferredcites →https://doi.org/10.1142/s0218195991000049openalex-snapshot
THE COMPLEXITY OF COMPUTING PARTIAL SUMS OFF-LINE
inferredcites →https://doi.org/10.1145/12130.12173openalex-snapshot
Further applications of random sampling to computational geometry
inferredcites →https://doi.org/10.1145/142675.142732openalex-snapshot
Range searching with efficient hierarchical cuttings
inferredcites →https://doi.org/10.1145/22145.22163openalex-snapshot
A general approach to d-dimensional geometric queries
inferredcites →https://doi.org/10.1145/322276.322281openalex-snapshot
A Lower Bound on the Complexity of Orthogonal Range Queries
inferredcites →https://doi.org/10.1145/73393.73394openalex-snapshot
Applications of random sampling in computational geometry, II
inferredcites →https://doi.org/10.1145/77600.77614openalex-snapshot
Lower bounds for orthogonal range searching: I. The reporting case
inferredcites →https://doi.org/10.1145/79147.79149openalex-snapshot
Lower bounds for orthogonal range searching: part II. The arithmetic model
inferredcites →https://doi.org/10.1145/800061.808755openalex-snapshot
A 3-space partition and its applications
inferredcites →https://doi.org/10.2307/1969800openalex-snapshot
A Theorem on Non-Homogeneous Lattices
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
inferred← citeshttps://doi.org/10.1007/978-3-030-11509-8_1openalex-snapshot
New Directions in Approximate Nearest-Neighbor Searching
inferred← citeshttps://doi.org/10.1007/978-3-319-44479-6_1openalex-snapshot
Simplex Range Searching and Its Variants: A Review
inferred← citeshttps://doi.org/10.1007/978-3-540-73951-7_2openalex-snapshot
Approximate Range Searching: The Absolute Model
inferred← citeshttps://doi.org/10.1007/bf02712875openalex-snapshot
New lower bounds for Hopcroft's problem
inferred← citeshttps://doi.org/10.1007/bfb0019430openalex-snapshot
Orders, k-sets and fast halfplane search on paged memory
inferred← citeshttps://doi.org/10.1007/s00454-009-9140-zopenalex-snapshot
The Effect of Corners on the Complexity of Approximate Range Searching
inferred← citeshttps://doi.org/10.1007/s00454-012-9412-xopenalex-snapshot
Tight Lower Bounds for Halfspace Range Searching
inferred← citeshttps://doi.org/10.1007/s00454-016-9845-8openalex-snapshot
$$\varepsilon $$ ε -Mnets: Hitting Geometric Set Systems with Subsets
inferred← citeshttps://doi.org/10.1007/s00454-016-9856-5openalex-snapshot
On the Combinatorial Complexity of Approximating Polytopes
inferred← citeshttps://doi.org/10.1007/s00454-023-00574-1openalex-snapshot
On Semialgebraic Range Reporting
inferred← citeshttps://doi.org/10.1007/s00454-025-00780-zopenalex-snapshot
Optimal Volume-Sensitive Bounds for Polytope Approximation
inferred← citeshttps://doi.org/10.1007/s00454-025-00815-5openalex-snapshot
Optimal Area-Sensitive Bounds for Polytope Approximation
inferred← citeshttps://doi.org/10.1016/b978-012088469-8.50077-2openalex-snapshot
Efficient Indexing Methods for Probabilistic Threshold Queries over Uncertain Data
inferred← citeshttps://doi.org/10.1016/j.comgeo.2007.05.008openalex-snapshot
Approximate range searching in higher dimension
inferred← citeshttps://doi.org/10.1016/j.comgeo.2008.09.009openalex-snapshot
Approximate range searching: The absolute model
inferred← citeshttps://doi.org/10.1016/j.dam.2018.05.049openalex-snapshot
Efficient independent set approximation in unit disk graphs
inferred← citeshttps://doi.org/10.1016/s0925-7721(00)00022-5openalex-snapshot
Approximate range searching☆☆A preliminary version of this paper appeared in the Proc. of the 11th Annual ACM Symp. on Computational Geometry, 1995, pp. 172–181.
inferred← citeshttps://doi.org/10.1109/focs46700.2020.00074openalex-snapshot
Polynomial Data Structure Lower Bounds in the Group Model
inferred← citeshttps://doi.org/10.1109/iv.2012.85openalex-snapshot
Solving the Range Searching Problem for Region Bounded by a Convex Surface
inferred← citeshttps://doi.org/10.1109/sfcs.1996.548506openalex-snapshot
New lower bounds for halfspace emptiness
inferred← citeshttps://doi.org/10.1109/sfcs.2002.1181892openalex-snapshot
An inverse-Ackermann style lower bound for the online minimum spanning tree verification problem
inferred← citeshttps://doi.org/10.1137/060669474openalex-snapshot
On Approximating the Depth and Related Problems
inferred← citeshttps://doi.org/10.1137/1.9781611974782.18openalex-snapshot
Optimal Approximate Polytope Membership
inferred← citeshttps://doi.org/10.1137/1.9781611977554.ch70openalex-snapshot
Economical Convex Coverings and Applications
inferred← citeshttps://doi.org/10.1137/20m1381988openalex-snapshot
Polynomial Data Structure Lower Bounds in the Group Model
inferred← citeshttps://doi.org/10.1137/23m1568351openalex-snapshot
Economical Convex Coverings and Applications
inferred← citeshttps://doi.org/10.1137/s0097539798337212openalex-snapshot
Space-Time Tradeoffs for Emptiness Queries
inferred← citeshttps://doi.org/10.1145/1132516.1132598openalex-snapshot
On the importance of idempotence
inferred← citeshttps://doi.org/10.1145/1810959.1810964openalex-snapshot
Tight lower bounds for halfspace range searching
inferred← citeshttps://doi.org/10.1145/220279.220293openalex-snapshot
New lower bounds for Hopcroft's problem
inferred← citeshttps://doi.org/10.1145/2213836.2213882openalex-snapshot
Processing a large number of continuous preference top- k queries
inferred← citeshttps://doi.org/10.1145/2261250.2261305openalex-snapshot
Optimal area-sensitive bounds for polytope approximation
inferred← citeshttps://doi.org/10.1145/3559106openalex-snapshot
Optimal Bound on the Combinatorial Complexity of Approximating Polytopes
inferred← citeshttps://doi.org/10.4230/lipics.itcs.2022.59openalex-snapshot
Uniform Brackets, Containers, and Combinatorial Macbeath Regions
inferred← citeshttps://doi.org/10.7561/sacs.2019.1.81openalex-snapshot
Enumerating Collinear Points in Higher Dimensions
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