Question

Having been learning data-structure and algorithm for a long time, I’m still uncertain about the practical application of those famous data-structure such as red-black tree, splay tree.

I know that B-tree has been widely used in database stuff.
With respect to other tree data-structure like red-black tree and splay tree etc,

1. have they been widely used in practice? If any, give some example.
2. Unlike B-tree whose structure can be retained and saved in disk, red-black and splay tree cannot achieve that, they are just in-memory structure, right? So how can they be as popular as B-tree?

Answer 1

I know that B-tree has been widely used in database stuff.

That isn’t very specific, is it?

In fact, B trees and red-black trees serve the exact same purpose: Both are index data structures, more precisely search trees, i.e. data structures that allow you to efficiently search for an item in a collection.

The only relevant difference between red-black trees and B trees is the fact that the latter incorporate some additional factors that improve their caching behaviour, which is required when access to memory is particularly slow due to high latency (simply put, an average access to the B tree will require less jumping around in memory than it does in the red-black tree, and more reading of adjacent memory locations, which is often much faster).

Historically, this has been used to store the index on a disk (secondary storage) which is very slow compared to main storage (RAM). Red-black trees, on the other hand, are often used when the index is retained in RAM (for example, the C++ std::map structure is usually implemented as a red-black tree).

This is going to change, though. Modern CPUs use caches to improve access to main memory further, and since acesss to the RAM is much slower than the cache, B trees (and their variants) once again become better suited than red-black trees.