Self-adjusting binary search trees
Journal of the ACM (JACM)
Computational geometry: an introduction
Computational geometry: an introduction
Optimal point location in a monotone subdivision
SIAM Journal on Computing
A data structure for dynamic trees
Journal of Computer and System Sciences
Making data structures persistent
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
A linear-time algorithm for computing the Voronoi diagram of a convex polygon
Discrete & Computational Geometry
The farthest point Delaunay triangulation minimizes angles
Computational Geometry: Theory and Applications
Design of Dynamic Data Structures
Design of Dynamic Data Structures
A dynamic data structure for 3-d convex hulls and 2-d nearest neighbor queries
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Farthest-point queries with geometric and combinatorial constraints
Computational Geometry: Theory and Applications
Computational Geometry: Theory and Applications
Compressing spatio-temporal trajectories
Computational Geometry: Theory and Applications
Compressing spatio-temporal trajectories
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Applications of forbidden 0-1 matrices to search tree and path compression-based data structures
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Semialgebraic Range Reporting and Emptiness Searching with Applications
SIAM Journal on Computing
CGGA'10 Proceedings of the 9th international conference on Computational Geometry, Graphs and Applications
Two-Dimensional range diameter queries
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Hi-index | 0.00 |
We consider preprocessing a set S of n points in the plane that are in convex position into a data structure supporting queries of the following form: given a point q and a directed line ℓ in the plane, report the point of S that is farthest from (or, alternatively, nearest to) the point q subject to being to the left of line ℓ. We present two data structures for this problem. The first data structure uses O(n1+ε) space and preprocessing time, and answers queries in O(21/ε log n) time. The second data structure uses O(n log3n) space and polynomial preprocessing time, and answers queries in O(log n) time. These are the first solutions to the problem with O(log n) query time and o(n2) space. In the process of developing the second data structure, we develop a new representation of nearest-point and farthest-point Voronoi diagrams of points in convex position. This representation supports insertion of new points in counterclockwise order using only O(log n) amortized pointer changes, subject to supporting O(log n)-time point-location queries, even though every such update may make Θ(n) combinatorial changes to the Voronoi diagram. This data structure is the first demonstration that deterministically and incrementally constructed Voronoi diagrams can be maintained in o(n) pointer changes per operation while keeping O(log n)-time point-location queries.