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I know there exists a technique to bulk load sorted data in a B+ tree.

However, I read at some places that there are 2 ways how bulk-loading can be approached - top-down and bottom-up. Resource (1) mentions that in the top-down approach, most of the internal nodes are sparse/half-full and none of the old entries go into a newer node. Whereas, in the bottom-up approach we can circumvent the sparsity.

Now, resource (2) discusses this bulk-loading technique in its own words, yet it is similar to resource (1). However, resource (2) proceeds to visualize how this bulk-loading can be implemented and ends up with a B+ tree with half-full nodes.

My question is

  1. Which of the resource is correct?
  2. How exactly is a top-down build different from a bottom-up build when considered for bulk-loading?
  3. Am I reading all of it wrong and bulk-loading is implemented with a bottom-up approach only? (Resource (2) says that the bottom-up approach is implemented as a part of bulk-load utility)

Resources:

  1. https://db-coder.github.io/DBInternalsReport.pdf
  2. https://slideplayer.com/slide/15127631/
  3. https://en.wikipedia.org/wiki/B-tree#Initial_construction

Note: Resource (2) is built with reference from the book Database Management Systems, (3rd edition), by Raghu Ramakrishnan and Johannes Gehrke. McGraw Hill, 2003.

I have given a thorough reading to the above-mentioned resources and other similar content online. Well, the only thing I did not do yet is asking ChatGPT.

Saasha Joshi
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  • I also found another reference for bulk loading on Wikipedia (Resource 3 in question), however, this is a highly un-cited paragraph there. The section "Initial Construction" for B Tree says that while bulk-loading we can split the nodes unevenly, ignoring the usual B Tree rules. As a result, the leftmost parent node is entirely full and the right node has zero keys and one child (which I assume is the node added using the bottom-up bulk-loading method). So in the end, we have a set of complete nodes except the last (rightmost) node which might be empty/less full. – Saasha Joshi Apr 06 '23 at 08:43

1 Answers1

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they describe two different approaches to bulk-loading a B+ tree and both are correct

  • top-down approach -- algorithm starts with an empty tree and inserts the keys in sorted order -- splitting full nodes as necessary(can result in many sparse (half-full) internal nodes -- as the algorithm may split nodes before they reach their maximum capacity)

  • bottom-up approach -- algorithm builds a set of leaf nodes with sorted data and then constructs the internal nodes recursively by merging pairs of leaf nodes and promoting their median key(more densely packed internal nodes -- does not split nodes until they contain the maximum number of keys)

both approaches have their advantages and disadvantages -- the choice depends on factors such as the size of the data set | expected access patterns | available hardware resources(some implementations may even use a hybrid approach)

Lemonina
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  • I understand your point here. But for the Top-down approach are we considering adding one key at a time or bulk-loading it node by node? Does node by node insertion exist? – Saasha Joshi Apr 04 '23 at 00:51
  • we generally add one key at a time - node by node insertion can also be used to build the B+tree but it isn't generally used for bulk-loading( node by node insertion involves adding a single key to the tree and then adjusting the tree structure as necessary to maintain the B+ tree properties - it can result in many splits and rearrangements of the tree structure - inefficient for bulk-loading large datasets) – Lemonina Apr 05 '23 at 07:12