STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Dealing with higher dimensions: the well-separated pair decomposition and its applications
Dealing with higher dimensions: the well-separated pair decomposition and its applications
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
External-memory graph algorithms
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Algorithms for dynamic closest pair and n-body potential fields
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Faster algorithms for some geometric graph problems in higher dimensions
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
On showing lower bounds for external-memory computational geometry problems
External memory algorithms
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
Topology B-Trees and Their Applications
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
Optimal parallel all-nearest-neighbors using the well-separated pair decomposition
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
External-memory computational geometry
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Randomized and deterministic algorithms for geometric spanners of small diameter
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
External Memory Data Structures
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
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 external memory algorithm to compute a well-separated pair decomposition (WSPD) of a given point set P in Rd in O(sort(N)) I/Os using O(N/B) blocks of external memory, where N is the number of points in P, and sort(N) denotes the I/O complexity of sorting N items. (Throughout this paper we assume that the dimension d is fixed). We also show how to dynamically maintain the WSPD in O(logB N) I/O's per insert or delete operation using O(N/B) blocks of external memory. As applications of the WSPD, we show how to compute a linear size t-spanner for P within the same I/O and space bounds and how to solve the K-nearest neighbor and K-closest pair problems in O(sort(KN)) and O(sort(N+K)) I/Os using O(KN/B) and O((N+K)/B) blocks of external memory, respectively. Using the dynamic WSPD, we show how to dynamically maintain the closest pair of P in O(logBN) I/O's per insert or delete operation using O(N/B) blocks of external memory.