Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
Computational geometry: an introduction
Computational geometry: an introduction
Maintenance of geometric extrema ∈
Journal of the ACM (JACM)
New upper bounds in Klee's measure problem
SIAM Journal on Computing
Minimum diameter spanning trees and related problems
SIAM Journal on Computing
Reporting points in halfspaces
Computational Geometry: Theory and Applications
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
Average case analysis of dynamic geometric optimization
Computational Geometry: Theory and Applications
Incremental and decremental maintenance of planar width
Journal of Algorithms
A fully dynamic algorithm for planar
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Design of Dynamic Data Structures
Design of Dynamic Data Structures
Dynamic subgraph connectivity with geometric applications
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Facility Location and the Geometric Minimum-Diameter Spanning Tree
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Facility location and the geometric minimum-diameter spanning tree
Computational Geometry: Theory and Applications - Special issue on computational geometry - EWCG'02
Dynamic algorithms for approximating interdistances
Nordic Journal of Computing
Dynamic algorithms for approximating interdistances
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
On Klee's measure problem for grounded boxes
Proceedings of the twenty-eighth annual symposium on Computational geometry
Minimum diameter cost-constrained Steiner trees
Journal of Combinatorial Optimization
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We give the first nontrivial worst-case results for dynamic versions of various basic geometric optimization and measure problems under the semi-online model, where during the insertion of an object we are told when the object is to be deleted. Problems that we can solve with sublinear update time include the Hausdorff distance of two point sets, discrete 1-center, largest empty circle, convex hull volume in three dimensions, volume of the union of axis-parallel cubes, and minimum enclosing rectangle. The decision versions of the Hausdorff distance and discrete 1-center problems can be solved fully dynamically. Some applications are mentioned.