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For many varied reasons, I decided to write my own balanced binary tree library. One feature of my library that I haven't seen in other freely available libraries is "clusters", and a "recluster" function.

The problem that I am attacking is that as elements are randomly added to the tree, the tree rotations that automatically happen to keep the tree balanced tend to spread the edge pointers all over the place. The end result is that in a large tree, a typical traversal can require reading nodes from all over physical memory (or disk pages): a very inefficient use of cache. By clustering several subtree "near the root nodes" together in physical memory, tree traversals can be sped-up significantly by keeping nodes that always get visited near one another within physical memory (or on the same disk page). For example, in a properly clustered tree, with clusters large enough to hold 4 levels of records (1+2+4+8 = 15 records), a tree of height 16 (>45000 records) can be traversed in only 4 cluster reads instead of 16 reads that might be required of a non-clustered tree.

What I don't know is a good way to measure how "out-of-cluster" a tree is. I'd like to be able to determine when a tree needs to be reclustered. I'm sure there is good theory out there for this; and the idea doesn't seem to be that difficult, but I haven't run onto the solution yet. I've spent a little bit of time googling for a method, and probably a couple of hours thinking about it. Nothing yet.

Any ideas or helpful links?


1 solution

Have you ever considered B+ trees as implemented by "The C Database Tool Chest", Mix Software. Mix is still on the web - Google "Mix Software". Note that the term "database" is, in fact, just a B+ tree. The database is a tree of memory or file blocks which contain multiple keys and records.

I got this in '85 and have used it ever since. I got the source software (don't know if this is still available). Not Open Source, but any programs that are released can be used without any royalty, only restriction is that it must be linked into an object, no DLLs, and the neither the source nor the library can be released - only the executable with the embedded code. With the source, you can make any modifications you want.

I modified it (originally 16bit - used Borland C to compile) to now use VS2008 thus 32 bit and supports >4GB files. Major rewrite to unwind the INT usage which now is 32 bit - in 16 bit an INT was 16 bit. Many conflicts with structure layout, and old 16 bit databases couldn't be read with the 32 bit version, nor the other way around. I built my version where I could declare which size of INT I wanted so I had only one converter to work with. I created two converters (16 bit and 32 bit) which could read the appropriate data base (in ascending order) and output a flat file with the data it contained, and then read in the flat file and write the other bit sized database.

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