On Finding the Maxima of a Set of Vectors
Journal of the ACM (JACM)
An Optimal Algorithm for Finding the Kernel of a Polygon
Journal of the ACM (JACM)
A New Convex Hull Algorithm for Planar Sets
ACM Transactions on Mathematical Software (TOMS)
An optimal real-time algorithm for planar convex hulls
Communications of the ACM
Convex hulls of finite sets of points in two and three dimensions
Communications of the ACM
Algorithms + Data Structures = Programs
Algorithms + Data Structures = Programs
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
A lower bound to finding convex hulls
A lower bound to finding convex hulls
Computational geometry.
Combinatorial Algorithms: Theory and Practice
Combinatorial Algorithms: Theory and Practice
A Bibliography on Digital and Computational Convexity (1961-1988)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image Computations on Meshes with Multiple Broadcast
IEEE Transactions on Pattern Analysis and Machine Intelligence
Maintenance of the set of segments visible from a moving viewpoint in two dimensions
Proceedings of the twelfth annual symposium on Computational geometry
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Computational Geometry on a Systolic Chip
IEEE Transactions on Computers
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For a number of common configurations of points (lines) in the plane, we develop datastructures in which insertions and deletions of points (or lines, respectively) can be processed rapidly without sacrificing much of the efficiency of query answering of known static structures for these configurations. As a main result we establish a fully dynamic maintenance algorithm for convex hulls that can process insertions and deletions of single points in only O(log3n) steps or less per transaction, where n is the number of points currently in the set. The algorithm has several intriguing applications, including that one can “peel” a set of n points in only O(log3n) steps and that one can maintain two sets at a costs of only O(log3n) or less per insertion and deletion such that it never takes more than O(log2n) steps to determine whether the two sets are separable by a straight line. Also efficient algorithms are obtained for dynamically maintaining the common intersection of a set of half-spaces and for dynamically maintaining the maximal elements of a set of plane points. The results are all derived by means of one master technique, which is applied repeatedly and which seems to capture an appropriate notion of “decomposability” for configurations.