Approximation algorithms for shortest path motion planning
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Classes of graphs which approximate the complete Euclidean graph
Discrete & Computational Geometry
Euclidean spanners: short, thin, and lanky
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Efficient 3-D range searching in external memory
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Efficient algorithms for constructing fault-tolerant geometric spanners
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On two-dimensional indexability and optimal range search indexing
PODS '99 Proceedings of the eighteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
External-memory graph algorithms
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Theory and practice of I/O-efficient algorithms for multidimensional batched searching problems
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
On showing lower bounds for external-memory computational geometry problems
External memory algorithms
Sparse communication networks and efficient routing in the plane (extended abstract)
Proceedings of the nineteenth annual ACM symposium on Principles of distributed computing
The Buffer Tree: A New Technique for Optimal I/O-Algorithms (Extended Abstract)
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
New Results of Fault Tolerant Geometric Spanners
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
Geometric Searching in Walkthrough Animations with Weak Spanners in Real Time
ESA '98 Proceedings of the 6th Annual European Symposium on Algorithms
Optimal dynamic interval management in external memory
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
External-memory computational geometry
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
I/O-Efficiently pruning dense spanners
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
| Hi-index | 0.00 |
We present an algorithm to answer a set Q of range counting queries over a point set P in d dimensions. The algorithm takes O (sort(|P| + |Q|) + (|P|+|Q|)α(|P|)/DB log M/Bd-1 |P|+|Q/B) I/Os and uses linear space. For an important special case, the α(|P|) term in the I/O-complexity of the algorithm can be eliminated. We apply this algorithm to constructing t-spanners for point sets in Rd and polygonal obstacles in the plane, and finding the K closest pairs of a point set in Rd.