Advantage of B+ trees over BSTs?
I'm learning about B+ trees in a class about databases and I was wondering what concrete advantages B+ trees would give over Binary Search Trees?
It seems like they both have O(logN) average complexity for most operations of note but B+ trees also have an additional (negligible?) search time at each child node where BSTs obviously only take O(1) time to figure out which child node to advance to.
What real-world advantages make B+ trees more popular in databases than BSTs?
Answer
The major advantage of the B+ tree (and B-trees in general) over binary search trees is that they play well with caches. If you have a binary search tree whose nodes are stored in more or less random order in memory, then each time you follow a pointer, the machine will have to pull in a new block of memory into the processor cache, which is dramatically slower than accessing memory already in cache.
The B+-tree and the B-tree work by having each node store a huge number of keys or values and have a large number of children. They are typically packed together in a way that makes it possible for a single node to fit nicely into cache (or, if stored on disk, to be pulled from the disk in a single read operation). You then have to do more work to find a key within the node or determine which child to read next, but because all memory accesses done on a single node can be done without going back to disk, the access times are very small. This means that even though in principle a BST might be better in terms of number of memory accesses, the B+-tree and the B-tree can performed better in terms of the runtime of those memory accesses.
The typical use case for a B+-tree or B-tree is in a database, where there is a huge amount of information and the data are so numerous that they can't all fit into main memory. Accordingly, the data can then be stored in a B+-tree or B-tree on a hard disk somewhere. This minimizes the number of disk reads necessary to pull in the data during lookups. Some filesystems (like ext4, I believe) use B-trees as well for the same reason - they minimize the number of disk lookups necessary, which is the real bottleneck.
Hope this helps!