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| Content Provider | Society for Industrial and Applied Mathematics (SIAM) |
|---|---|
| Author | Smid, Michiel Golin, Mordecai Schwarz, Christian Raman, Rajeev |
| Copyright Year | 1998 |
| Abstract | We describe a new randomized data structure, the sparse partition, for solving the dynamic closest-pair problem. Using this data structure the closest pair of a set of n points in D-dimensional space, for any fixed D, can be found in constant time. If a frame containing all the points is known in advance, and if the floor function is available at unit cost, then the data structure supports insertions into and deletions from the set in expected O(log n) time and requires expected O(n) space. This method is more efficient than any deterministic algorithm for solving the problem in dimension D > 1. The data structure can be modified to run in O(log2n) expected time per update in the algebraic computation tree model. Even this version is more efficient than the best currently known deterministic algorithm for D > 2. Both results assume that the sequence of updates is not determined in any way by the random choices made by the algorithm. |
| Starting Page | 1036 |
| Ending Page | 1072 |
| Page Count | 37 |
| File Format | |
| ISSN | 00975397 |
| DOI | 10.1137/S0097539794277718 |
| e-ISSN | 10957111 |
| Journal | SIAM Journal on Computing (SMJCAT) |
| Issue Number | 4 |
| Volume Number | 27 |
| Language | English |
| Publisher | Society for Industrial and Applied Mathematics |
| Publisher Date | 2006-07-28 |
| Access Restriction | Subscribed |
| Subject Keyword | proximity randomization Computer graphics; computational geometry computational geometry dynamic data structures |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics Computer Science |
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