i2bplustree
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A package to implement the Improved Interval B+ tree, in TypeScript
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# Improved Interval B+ tree implementation (_I2B+ tree_)
[](https://bettercodehub.com/)
[](https://travis-ci.com/most-inesctec/I2Bplus-tree)
[](https://coveralls.io/github/most-inesctec/I2Bplus-tree?branch=master)
The ___Interval B+ tree (IB+ tree)___ is a valid-time indexing structure, first introduced by [Bozkaya and Ozsoyoglu](https://www.researchgate.net/publication/221465339_Indexing_Valid_Time_Intervals). This indexing structure appears as a time-efficient indexing structure for the management of valid-time/ intervals.
In this repository, we present the ___Improved Interval B+ tree (I2B+ tree)___, an indexing structure based on the _IB+ tree_, but with minor structural changes to improve the performance of the deletion operation. For a more detailed analysis of the _I2B+ tree_, refer to the paper published in the [CISTI'2020 Conference](http://www.cisti.eu), available at [__IEEE__](https://ieeexplore.ieee.org/document/9140897).
This structure performs all operations (insertion, search and deletion) with logarithmic performance (_O (log n)_). Documentation is available [here](https://edgaracarneiro.github.io/I2Bplus-tree/).
| Insertion | Range Search | Deletion |
|:-:|:-:|:-:|
|  |  |  |
For an in-depth analysis of both the parameter tuning (such as the tree's order or the time-splits alpha value) and the conclusions obtained from the performance analysis of the _I2B+ tree_, check the [benchmarks folder](https://github.com/EdgarACarneiro/IBplusTree/tree/master/benchmarks).
# Usage
To suit the _I2BplusTree_ to your needs, implement a class that __extends the [FlatInterval](https://github.com/EdgarACarneiro/IBplusTree/blob/master/src/FlatInterval.ts)__ class, defining the information that will be stored on leaves there. One might also want to override the `equals` method, thus allowing the incorporation of the extra information stored in the Intervals in comparisons.
Example:
```TypeScript
import { IBplusTree, FlatInterval } from 'i2bplustree';
// Create a class that inherits from the FlatInterval
class MyInterval extends FlatInterval {
// This is just an example property
// Like this there could be many more
private myProperty: any;
constructor(val1: number, val2: number, myPropertyValue: any) {
super(val1, val2);
this.myProperty = myPropertyValue;
}
// This is just an example method
public exampleMethod(): void {
// Do stuff
}
// Overriding equals method to take into account the new property
equals(int: MyInterval): boolean {
return this.upperBound == int.getUpperBound() &&
this.lowerBound == int.getLowerBound() &&
this.myProperty == int.getProperty();
}
}
// Now we create our I2BplusTree object and insert a `MyInterval` object
const threshold = 30;
const alpha = 0.2;
const tree: IBplusTree<MyInterval> = new IBplusTree<MyInterval>(threshold, alpha);
// Introduce an object
tree.insert(new MyInterval(0, 2, "example-property"));
/**
And do many other operations such as:
- Delete an interval from the tree
- Delete all intervals contained in a range
- Verify if a interval exists in the tree
- Search all intervals with equal bounds to the ones provided
- Find the first interval that intersects the given bounds
- Find all intervals intersecting the given range
- Find all intervals contained in the given range
*/
```
# Acknowledgements
This work was financed by the ERDF – European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT - Fundação para a Ciência e a Tecnologia within project PTDC/CCI-INF/32636/2017 (POCI-01-0145-FEDER-032636).
This work is also part of [MOST](http://most.web.ua.pt).
# Citation
> E. Carneiro, A. V. d. Carvalho and M. A. Oliveira, "I2B+tree: Interval B+ tree variant towards fast indexing of time-dependent data," 2020 15th Iberian Conference on Information Systems and Technologies (CISTI), Sevilla, Spain, 2020, pp. 1-7, doi: 10.23919/CISTI49556.2020.9140897.
OR
> Carneiro, Edgar, Alexandre Valle de Carvalho, and Marco Amaro Oliveira. "A Comparative Study on the Performance of the IB+ Tree and the I2B+ Tree." Journal of Information Systems Engineering and Management 6.3 (2021): em0142.