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
Applications of random sampling in computational geometry, II
Discrete & Computational Geometry - Selected papers from the fourth ACM symposium on computational geometry, Univ. of Illinois, Urbana-Champaign, June 6 8, 1988
Maintenance of geometric extrema ∈
Journal of the ACM (JACM)
Dynamic maintenance of geometric structures made easy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Fully dynamic Delaunay triangulation in logarithmic expected time per operation
Computational Geometry: Theory and Applications
Reporting points in halfspaces
Computational Geometry: Theory and Applications
Four results on randomized incremental constructions
Computational Geometry: Theory and Applications
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Deterministic algorithms for 2-D convex programming and 3-D Online linear programming
Journal of Algorithms
On range reporting, ray shooting and k-level construction
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Fast hierarchical clustering and other applications of dynamic closest pairs
Journal of Experimental Algorithmics (JEA)
Incremental and decremental maintenance of planar width
Journal of Algorithms
Dynamic planar convex hull operations in near-logarithmic amortized time
Journal of the ACM (JACM)
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Semi-Online Maintenance of Geometric Optima and Measures
SIAM Journal on Computing
Low-Dimensional Linear Programming with Violations
SIAM Journal on Computing
Kinetic 3D convex hulls via self-adjusting computation
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
On bounded leg shortest paths problems
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
VLDB '07 Proceedings of the 33rd international conference on Very large data bases
In-place 2-d nearest neighbor search
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Power efficient resilience and lifetime in wireless ad-hoc networks
Proceedings of the 1st ACM international workshop on Foundations of wireless ad hoc and sensor networking and computing
Proceedings of the twenty-fourth annual symposium on Computational geometry
On construction of minimum energy k-fault resistant topologies
Ad Hoc Networks
Optimal halfspace range reporting in three dimensions
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Multi cover of a polygon minimizing the sum of areas
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Online geometric reconstruction
Journal of the ACM (JACM)
Three problems about dynamic convex hulls
Proceedings of the twenty-seventh annual symposium on Computational geometry
Dynamic Connectivity: Connecting to Networks and Geometry
SIAM Journal on Computing
Data structures for halfplane proximity queries and incremental voronoi diagrams
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
Range searching on uncertain data
ACM Transactions on Algorithms (TALG)
Kinetic Euclidean minimum spanning tree in the plane
Journal of Discrete Algorithms
Computational Geometry: Theory and Applications
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Collective spatial keyword queries: a distance owner-driven approach
Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data
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We present a fully dynamic randomized data structure that can answer queries about the convex hull of a set of n points in three dimensions, where insertions take O(log3 n) expected amortized time, deletions take O(log6 n) expected amortized time, and extreme-point queries take O(log2 n) worst-case time. This is the first method that guarantees polylogarithmic update and query cost for arbitrary sequences of insertions and deletions, and improves the previous O(nε)-time method by Agarwal and Matoušek a decade ago. As a consequence, we obtain similar results for nearest neighbor queries in two dimensions and improved results for numerous fundamental geometric problems (such as levels in three dimensions and dynamic Euclidean minimum spanning trees in the plane).