UB-tree
| UB-tree | |||||
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| Type | tree | ||||
| Invented by | Rudolf Bayer and Volker Markl | ||||
| Time complexity in big O notation | |||||
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The UB-tree as proposed by Rudolf Bayer and Volker Markl is a balanced tree for storing and efficiently retrieving multidimensional data. It is basically a B+ tree (information only in the leaves) with records stored according to Z-order, also called Morton order. Z-order is simply calculated by bitwise interlacing the keys.
Insertion, deletion, and point query are done as with ordinary B+ trees. To perform range searches in multidimensional point data, however, an algorithm must be provided for calculating, from a point encountered in the data base, the next Z-value which is in the multidimensional search range.
The original algorithm to solve this key problem was exponential with the dimensionality and thus not feasible[1] ("GetNextZ-address"). A solution to this "crucial part of the UB-tree range query" linear with the z-address bit length has been described later.[2] This method has already been described in an older paper[3] where using Z-order with search trees has first been proposed.
References
- ↑ Markl, V. (1999). "MISTRAL: Processing Relational Queries using a Multidimensional Access Technique". CiteSeerX 10.1.1.32.6487.
- ↑ Ramsak, Frank; Markl, Volker; Fenk, Robert; Zirkel, Martin; Elhardt, Klaus; Bayer, Rudolf (September 10–14, 2000). "Integrating the UB-tree into a Database System Kernel". 26th International Conference on Very Large Data Bases. pp. 263–272. http://www.vldb.org/conf/2000/P263.pdf.
- ↑ Tropf, H.; Herzog, H.. "Multidimensional Range Search in Dynamically Balanced Trees". Angewandte Informatik (Applied Informatics) (2/1981): 71–77. ISSN 0013-5704. http://www.vision-tools.com/h-tropf/multidimensionalrangequery.pdf.
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