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https://github.com/jiayuasu/stx-btree

Machine Learning based B+ Tree
https://github.com/jiayuasu/stx-btree

b-tree bplustree learned-database learned-database-components learned-index machine-learning

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Machine Learning based B+ Tree

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# Machine Learning based B+ Tree



This repo contains a Machine-Learning enhanced B+ Tree index. You can call it `learned B+ Tree` or `Model-based B+ Tree`. It replaces the data format of internal nodes with a linear regression model and a gapped array.



## Design



For each internal node, we first train a linear model on the `` pairs of data inside the node, then reoganize the positions of the pairs based on the model prediction.



The benefit is two-fold:



1. The binary search in each internal node is replaced by a prediction-based exponential search.

2. This does not consume more memory space compared to the original B+ Tree implementation. In most cases, a B+ Tree node is only around 50% - 70% full for the sake of insertion.



When a B+ node is close to full, the prediction-based search might be slightly worse than binary search. Because the accuracy of model prediction will downgrade while the performance of exponential search is highly affected by the starting position of the search.



## Usage



This implementation supports bulk-load and insertion.



Please read the test cases: https://github.com/jiayuasu/stx-btree/blob/master/testsuite/BulkLoadTest.cc



## Publication



The performance of this index is studied in our SIGMOD 2020 paper: 



> Ding, Jialin, Umar Farooq Minhas, Jia Yu, Chi Wang, Jaeyoung Do, Yinan Li, Hantian Zhang et al. "ALEX: an updatable adaptive learned index." In Proceedings of the 2020 ACM SIGMOD International Conference on Management of Data, pp. 969-984. 2020.



A PDF copy of this paper is available on ACM website: https://dl.acm.org/doi/pdf/10.1145/3318464.3389711



Figure 9 illustrates the performance of this Model B+ Tree:



Apache Sedona



---

# STX B+ Tree C++ Template Classes v0.9



Author: Timo Bingmann (Mail: tb a-with-circle panthema dot net)


Date: 2013-05-05



# **The STX B+ Tree package is obsolete.**



## The B+ Tree code was merged into the **TLX Library**:


https://github.com/tlx/tlx/tree/master/tlx/container



This is an improved version with **better STL semantics** and it will be maintain in the TLX library.



## Summary



The STX B+ Tree package is a set of C++ template classes implementing a B+ tree

key/data container in main memory. The classes are designed as drop-in

replacements of the STL containers set, map, multiset and multimap and follow

their interfaces very closely. By packing multiple value pairs into each node

of the tree the B+ tree reduces heap fragmentation and utilizes cache-line

effects better than the standard red-black binary tree. The tree algorithms are

based on the implementation in Cormen, Leiserson and Rivest's Introduction into

Algorithms, Jan Jannink's paper and other algorithm resources. The classes

contain extensive assertion and verification mechanisms to ensure the

implementation's correctness by testing the tree invariants. To illustrate the

B+ tree's structure a wxWidgets demo program is included in the source package.



## Website / API Docs / Bugs / License



The current source package can be downloaded from

http://panthema.net/2007/stx-btree/



The include files are extensively documented using doxygen. The compiled

doxygen html documentation is included in the source package. It can also be

viewed online at

http://panthema.net/2007/stx-btree/stx-btree-0.9/doxygen-html/



The wxWidgets B+ tree demo program is located in the directory

wxbtreedemo. Compiled binary versions can be found on the package web page.



If bugs should become known they will be posted on the above web page together

with patches or corrected versions.



The B+ tree template source code is released under the Boost Software License,

Version 1.0, which can be found at the header of each include file.



All auxiliary programs like the wxWidgets demo, test suite and speed tests are

licensed under the GNU General Public License v3 (GPLv3), which can be found in

the file COPYING.GPLv3.



## Original Idea



The idea originally arose while coding a read-only database, which used a huge

map of millions of non-sequential integer keys to 8-byte file offsets. When

using the standard STL red-black tree implementation this would yield millions

of 20-byte heap allocations and very slow search times due to the tree's

height. So the original intension was to reduce memory fragmentation and

improve search times. The B+ tree solves this by packing multiple data pairs

into one node with a large number of descendant nodes.



In computer science lectures it is often stated that using consecutive bytes in

memory would be more cache-efficient, because the CPU's cache levels always

fetch larger blocks from main memory. So it would be best to store the keys of

a node in one continuous array. This way the inner scanning loop would be

accelerated by benefiting from cache effects and pipelining speed-ups. Thus the

cost of scanning for a matching key would be lower than in a red-black tree,

even though the number of key comparisons are theoretically larger. This second

aspect aroused my academic interest and resulted in the speed test experiments.



A third inspiration was that no working C++ template implementation of a B+

tree could be found on the Internet. Now this one can be found.



## Implementation Overview



This implementation contains five main classes within the stx namespace

(blandly named Some Template eXtensions). The base class btree implements the

B+ tree algorithms using inner and leaf nodes in main memory. Almost all

STL-required function calls are implemented (see below for the exceptions). The

asymptotic time requirements of the STL standard are theoretically not always

fulfilled. However in practice this B+ tree performs better than the STL's

red-black tree at the cost of using more memory. See the speed test results for

details.



The base class is then specialized into btree_set, btree_multiset, btree_map

and btree_multimap using default template parameters and facade

functions. These classes are designed to be drop-in replacements for the

corresponding STL containers.



The insertion function splits the nodes on recursion unroll. Erase is largely

based on Jannink's ideas. See http://dbpubs.stanford.edu:8090/pub/1995-19 for

his paper on "Implementing Deletion in B+-trees".



The two set classes (btree_set and btree_multiset) are derived from the base

implementation class btree by specifying an empty struct as data_type. All

functions are adapted to provide the base class with empty placeholder

objects. Note that it is somewhat inefficient to implement a set or multiset

using a B+ tree: a plain B tree (without +) would hold no extra copies of the

keys. The main focus was on implementing the maps.



## Problem with Separated Key/Data Arrays



The most noteworthy difference to the default red-black tree implementation of

std::map is that the B+ tree does not hold key/data pairs together in

memory. Instead each B+ tree node has two separate arrays containing keys and

data values. This design was chosen to utilize cache-line effects while

scanning the key array.



However it also directly generates many problems in implementing the iterators'

operators. These return a (writable) reference or pointer to a value_type,

which is a std::pair composition. These data/key pairs however are not stored

together and thus a temporary copy must be constructed. This copy should not be

written to, because it is not stored back into the B+ tree. This effectively

prohibits use of many STL algorithms which writing to the B+ tree's

iterators. I would be grateful for hints on how to resolve this problem without

folding the key and data arrays.



## Test Suite



The B+ tree distribution contains an extensive test suite. According to gcov

90.9% of the btree.h implementation is covered.



## STL Incompatibilities



#### Key and Data Type Requirements



The tree algorithms currently do not use copy-construction. All key/data items

are allocated in the nodes using the default-constructor and are subsequently

only assigned new data (using operator=).



#### Key Iterators' Operators



The most important incompatibility are the non-writable operator* and

operator-> of the iterator. See above for a discussion of the problem on

separated key/data arrays. Instead of *iter and iter-> use the new function

iter.data() which returns a writable reference to the data value in the tree.



#### Key Erase Functions



The B+ tree supports three erase functions:



size_type erase(const key_type &key); // erase all data pairs matching key

bool erase_one(const key_type &key);  // erase one data pair matching key

void erase(iterator iter);            // erase pair referenced by iter



The following STL-required function is not supported:



void erase(iterator first, iterator last);



## Extensions



Beyond the usual STL interface the B+ tree classes support some extra goodies.



```

// Output the tree in a pseudo-hierarchical text dump to std::cout. This

// function requires that BTREE_DEBUG is defined prior to including the btree

// headers. Furthermore the key and data types must be std::ostream printable.

void print() const;



// Run extensive checks of the tree invariants. If a corruption in found the

// program will abort via assert(). See below on enabling auto-verification.

void verify() const;



// Serialize and restore the B+ tree nodes and data into/from a binary image.

// This requires that the key and data types are integral and contain no

// outside pointers or references.

void dump(std::ostream &os) const;

bool restore(std::istream &is);

```



## B+ Tree Traits



All tree template classes take a template parameter structure which holds

important options of the implementation. The following structure shows which

static variables specify the options and the corresponding defaults:



```

struct btree_default_map_traits

{

    // If true, the tree will self verify it's invariants after each insert()

    // or erase(). The header must have been compiled with BTREE_DEBUG

    // defined.

    static const bool   selfverify = false;



    // If true, the tree will print out debug information and a tree dump

    // during insert() or erase() operation. The header must have been

    // compiled with BTREE_DEBUG defined and key_type must be std::ostream

    // printable.

    static const bool   debug = false;



    // Number of slots in each leaf of the tree. Estimated so that each node

    // has a size of about 128 bytes.

    static const int    leafslots =

                             MAX( 8, 128 / (sizeof(_Key) + sizeof(_Data)) );



    // Number of slots in each inner node of the tree. Estimated so that each

    // node has a size of about 128 bytes.

    static const int    innerslots =

                             MAX( 8, 128 / (sizeof(_Key) + sizeof(void*)) );



    // As of stx-btree-0.9, the code does linear search in find_lower() and

    // find_upper() instead of binary_search, unless the node size is larger

    // than this threshold. See notes at

    // http://panthema.net/2013/0504-STX-B+Tree-Binary-vs-Linear-Search

    static const size_t binsearch_threshold = 256;

};

```



## Speed Tests



The implementation was tested using the speed test sources contained in the

package. For a long discussion on results please see the web page



http://panthema.net/2007/stx-btree/