Randomized K-dimensional binary search trees
This paper introduces randomized K-dimensional binary search trees (randomized Kd-trees), a variant of K-dimensional binary trees. This data structure allows the efficient maintenance of multidimensional records for any sequence of insertions and deletions; and thus, is fully dynamic. We show that s...
| Autores: | , , |
|---|---|
| Tipo de documento: | relatório científico |
| Data de publicação: | 1998 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositório: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglês |
| OAI Identifier: | oai:upcommons.upc.edu:2117/84547 |
| Acesso em linha: | https://hdl.handle.net/2117/84547 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Randomized algorithms Multidimensional data structures Kd-trees Multidimensional dictionaries Associative queries Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica |
| Resumo: | This paper introduces randomized K-dimensional binary search trees (randomized Kd-trees), a variant of K-dimensional binary trees. This data structure allows the efficient maintenance of multidimensional records for any sequence of insertions and deletions; and thus, is fully dynamic. We show that several types of associative queries are efficiently supported by randomized Kd-trees. In particular, a randomized Kd-tree with n records answers exact match queries in expected O(log n) time. Partial match queries are answered in expected O(n^{1-f(s/K)}) time, when s out of K attributes are specified, with 0 < f(s/K) < 1 a real valued function of s/K. Nearest neighbor queries are answered on-line in expected O(log n) time. Our randomized algorithms guarantee that their expected time bounds hold irrespective of the order and number of insertions and deletions. |
|---|