Gregory Trubetskoy

Notes to self.

Relational Database on Top of Key-value Store Explained (or Why B-trees Are Cool)

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This post attempts to explain how a relational database can be implemented atop a key/value store, a subject that I’ve long found rather mysterious.

Every once in a while I would come across a mention that a relational database can be implemented using a key/value store (aka dictionary, hash table or hash map - for brevity I’ll be using map from here on).

Whenever I thought about it, it just didn’t make sense. A relational database needs to store rows in order, and that’s one feature that maps do not provide. Imagine we have a table keyed by employee id stored in a map and we need to traverse it by id in ascending order. A hypothetical keys() method would return us a list of ids ordered randomly. It’s impossible to iterate over a hash map in order. So how would a relational database work then?

It took a while for me to realize the root of my misunderstanding. I naively was trying to picture how tables, rows and values can be represented as key/value pairs, and that was the wrong path to take. I was focusing on the wrong layer of abstraction.

As it turns out the key [NPI] to this problem is the clever data structure commonly used to store data in a relational DB known as B-Tree (or a variation thereof, B+Tree). Okay, B-trees are nothing new and I’m sure we’ve all heard of them. In fact B-trees were desgined in the 1970’s as a generalization of the Binary Search Tree that was more suited for block storage.

But there is something about B-trees that I did not know, and which now that I do know, seems absolutely essential as well as simply brilliant. In his 1979 paper “The Ubiquitous B-Tree” Douglas Comer writes:

The availability of demand paging hardware suggests an interesting implementation of B-trees. Through careful allocation, each node of the B-tree can be mapped into one page of the virtual address space. Then the user treats the B-tree as if it were in memory. Accesses to nodes (pages) which are not in memory cause the system to “page-in” the node from secondary storage.

The above paragraph implies that the B-Tree and all its data can be stored in pages. In fact, if you look at the file format of a SQLite 3 database (who says source code comments are bad?) you’ll see it states quite plainly that the file is divided into pages. (You will also see a fantastic description of exactly how a B+tree works, but that’s way outside the scope of this post.)

The important point is that the entire file consists of pages and nothing else. Inside those pages live the B-tree structure, as well as the data. Each table is a B-tree and to access it we need to know the starting page number, which in turn is stored in the sqlite_master table whose root page is always the first page of the file. The root page of a table is the head of the B-tree strucutre, and it may refer to other pages, which in turn may be additional nodes of the tree or pure data.

All pages are of the same size and are numbered sequentially, thus we can easily retreive any page by its number because its offset into the file is the page number multiplied by the page size. (By default a SQLite3 page is 1K and will hold 4 keys, i.e. the order of the tree is 4).

And bingo, there is our key/value pair: the page number is the key, and the page itself is the value! All you need to do is stick those pages into your favorite key/value store keyed by page number and you’ve got a relational database atop a key/value store. It’s that simple.

P.S. An astute reader may point out that there is such a thing as a sorted map. But a sorted map is very different from a “pure” hash map. The miracle of hashing is that not only does it let you find elements in O(1) time, but more importantly that it is very suitable for distributed processing, where the map may be spread across multiple servers. And if you start thinking about how a sorted map might be implemented in a distributed fashion, you will ultimately loop back to B-trees, because that’s typically how it’s actually done.