kindaro / diet-set

Implementation of Discrete Interval Encoding Trees in Haskell

Discrete Interval Encoding Trees

Description

Discrete Interval Encoding Trees[1], diet for short, allows sets containing consecutive values to represent those values as a single interval instead of individual elements. This could drastically cut down on the number of nodes needed.

Take for instance the set [2, 5, 6, 7, 8, 9, 10, 13, 14]. Using a normal binary tree with one value per element this could be represented as:

   +--14
   |
+--13
|  |
|  +--10
|
9
|
|     +--|
|     |
|  +--8
|  |  |
|  |  +--7
|  |
+--6
   |
   |  +--5
   |  |
   +--2
      |
      +--|

Using discrete interval encoding trees we instead get:

+--[13, 14]
|
[5, 10]
|
+--[2,2]

References

[1] Martin Erwig, Diets for Fat Sets, Journal of Functional Programming, Vol. 8, No. 6, 627-632, 1998