Computing the extreme distances between two convex polygons
Journal of Algorithms
Computational geometry: an introduction
Computational geometry: an introduction
Journal of Algorithms
SIGMOD '95 Proceedings of the 1995 ACM SIGMOD international conference on Management of data
On data structures and asymmetric communication complexity
Journal of Computer and System Sciences
A practical approach for computing the diameter of a point set
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Efficient Execution of Range-Aggregate Queries in Data Warehouse Environments
ER '01 Proceedings of the 20th International Conference on Conceptual Modeling: Conceptual Modeling
Scaling and related techniques for geometry problems
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
SIAM Journal on Computing
Approximating extent measures of points
Journal of the ACM (JACM)
Note: Fast set intersection and two-patterns matching
Theoretical Computer Science
Distance Oracles beyond the Thorup-Zwick Bound
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Range-aggregate queries involving geometric aggregation operations
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Orthogonal range searching on the RAM, revisited
Proceedings of the twenty-seventh annual symposium on Computational geometry
Algorithms for range-aggregate query problems involving geometric aggregation operations
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Data structures for halfplane proximity queries and incremental voronoi diagrams
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Algorithms for range-skyline queries
Proceedings of the 20th International Conference on Advances in Geographic Information Systems
Range-aggregate queries for geometric extent problems
CATS '13 Proceedings of the Nineteenth Computing: The Australasian Theory Symposium - Volume 141
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Given a set of n points in the plane, range diameter queries ask for the furthest pair of points in a given axis-parallel rectangular range. We provide evidence for the hardness of designing space-efficient data structures that support range diameter queries by giving a reduction from the set intersection problem. The difficulty of the latter problem is widely acknowledged and is conjectured to require nearly quadratic space in order to obtain constant query time, which is matched by known data structures for both problems, up to polylogarithmic factors. We strengthen the evidence by giving a lower bound for an important subproblem arising in solutions to the range diameter problem: computing the diameter of two convex polygons, that are separated by a vertical line and are preprocessed independently, requires almost linear time in the number of vertices of the smaller polygon, no matter how much space is used. We also show that range diameter queries can be answered much more efficiently for the case of points in convex position by describing a data structure of size O(nlogn) that supports queries in O(logn) time.