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In-Memory Trees in Mathematica
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| Organization: | University of Connecticut |
| Department: | Natural Resources Management and Engineering |
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Wolfram Technology Conference 2013
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Champaign, Illinois, USA
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Nested lists are one of Mathematica primary data structures, and nested lists are also called trees. However, Mathematica provides no explicit support for user-defined trees (other than TreePlot). A generic tree data structure is presented. The tree is polymorphic so it can be constructed from arbitrary objects (not just keys), which in essence implements a user-defined, in-memory database. The tree supports both unique and redundant keys that are handled with compound keys. Keys are ordered with a user-defined function, which allows trees like binary search trees or even more exotic spatial trees, like quadtrees. (However, this implementation does no balancing.)
Mathematica's unique functional language permits a single function for each fundamental operation: insertions, retrievals, deletions, and updates. The user provides functions to control the insertions, which is why a single generic suite of basic functions is sufficient for a very broad variety of trees. The code is presented along with several examples that illustrate some of the possibilities.
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http://www.wolfram.com/events/technology-conference/2013
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| WTC1013-TomMeyer.nb (457.7 KB) - Mathematica Notebook |
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