Computing the visibility graph of points within a polygon
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Kinetic collision detection with fast flight plan changes
Information Processing Letters
Polygonal chain approximation: a query based approach
Computational Geometry: Theory and Applications
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
An experimental analysis of self-adjusting computation
Proceedings of the 2006 ACM SIGPLAN conference on Programming language design and implementation
Proximity problems on line segments spanned by points
Computational Geometry: Theory and Applications
On finding a widest empty 1-corner corridor
Information Processing Letters
Optimal simplification of polygonal chain for rendering
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Tight bounds for dynamic convex hull queries (again)
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Buddy tracking - efficient proximity detection among mobile friends
Pervasive and Mobile Computing
Covering point sets with two disjoint disks or squares
Computational Geometry: Theory and Applications
Proceedings of the twenty-fourth annual symposium on Computational geometry
Output-sensitive algorithms for Tukey depth and related problems
Statistics and Computing
Optimal simplification of polygonal chains for subpixel-accurate rendering
Computational Geometry: Theory and Applications
Significance-Driven Graph Clustering
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
Uniquely Represented Data Structures for Computational Geometry
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Relative Convex Hulls in Semi-dynamic Subdivisions
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Improved upper bounds on the reflexivity of point sets
Computational Geometry: Theory and Applications
Divide and Conquer Method for k-Set Polygons
Computational Geometry and Graph Theory
CEAL: a C-based language for self-adjusting computation
Proceedings of the 2009 ACM SIGPLAN conference on Programming language design and implementation
On the Red/Blue Spanning Tree Problem
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
An experimental analysis of self-adjusting computation
ACM Transactions on Programming Languages and Systems (TOPLAS)
Proximity problems on line segments spanned by points
Computational Geometry: Theory and Applications
Optimal blurred segments decomposition of noisy shapes in linear time
Computers and Graphics
An algorithm for discrete approximation by quasi-convex functions on Rm
Computers & Mathematics with Applications
A dynamic data structure for 3-D convex hulls and 2-D nearest neighbor queries
Journal of the ACM (JACM)
A Library for Self-Adjusting Computation
Electronic Notes in Theoretical Computer Science (ENTCS)
Kinetic collision detection with fast flight plan changes
Information Processing Letters
On finding a widest empty 1-corner corridor
Information Processing Letters
Weighted rectilinear approximation of points in the plane
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Self-adjusting computation with Delta ML
AFP'08 Proceedings of the 6th international conference on Advanced functional programming
Dynamic one-sided boundary labeling
Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems
Stabbers of line segments in the plane
Computational Geometry: Theory and Applications
On the red/blue spanning tree problem
Theoretical Computer Science
FIFO indexes for decomposable problems
Proceedings of the thirtieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Three problems about dynamic convex hulls
Proceedings of the twenty-seventh annual symposium on Computational geometry
Connectivity guarantees for wireless networks with directional antennas
Computational Geometry: Theory and Applications
Delineating boundaries for imprecise regions
ESA'05 Proceedings of the 13th annual European conference on Algorithms
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
Outlier respecting points approximation
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Coloring half-planes and bottomless rectangles
Computational Geometry: Theory and Applications
All-maximum and all-minimum problems under some measures
Journal of Discrete Algorithms
Computational Geometry: Theory and Applications
Plane 3-trees: embeddability and approximation
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Distribution-based query scheduling
Proceedings of the VLDB Endowment
Monochromatic geometric k-factors for bicolored point sets with auxiliary points
Information Processing Letters
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In this paper we determine the computational complexity of the dynamic convex hull problem in the planar case. We present a data structure that maintains a finite set of n points in the plane under insertion and deletion of points in amortized O(log n) time per operation. Thespace usage of the data structure is O(n). The data structure supports extreme point queries in a given direction, tangent queries through a given point, and queries for the neighboring points on the convex hull in O(log n) time. The extreme point queries can be used to decide whether or not a given line intersects the convex hull, and the tangent queries to determine whether a given point is inside the convex hull. We give a lower bound on the amortized asymptotic time complexity that matches the performance of this data structure.