Joshua Nathaniel Pritikin

NAME

Tree::Fat - Perl Extension to Implement Fat-Node Trees

SYNOPSIS

This is not a plug-and-play perl extension. This module is designed for embedding (and there is no default embedding).

  1. tvgen.pl -p PREFIX

  2. Edit PREFIXtv.tmpl

  3. Compile and link into your own application!

DESCRIPTION

Implements object-oriented trees using algorithms adapted from b-trees and AVL trees (without resorting to yucky C++). Fat-node trees are not the best for many niche applications but they do have excellent all-terrain performance.

 TYPE       Speed       Flexibility  Scales     Memory   Keeps-Order
 ---------- ----------- ------------ ---------- -------- ------------
 Arrays     fastest     so-so        not good   MIN      yes
 Hashes     fast        good         so-so      so-so    no
 Fat-Trees  medium      silly        big        good     yes

WHAT IS A FAT-TREE?

It's a cross between a tree and an array. Each tree node contains a fixed length array of slots. Tree performance is enhanced by balancing array operations with tree operations. Moreover, tree operations are better optimized by taking the arrays into account.

HOW ABOUT PERSISTANCE?

F-Trees are designed for embedding. (If you want persistent F-Trees without the work, then check out the ObjStore extension by the same author. F-Trees are already integrated into the ObjectStore database, right now!)

CURSOR BEHAVIOR

The only way to access a tree is via a cursor. Cursors behavior is derived from the principle of least-surprise (rather than greatest efficiency). More documentation there isn't. Please read the source code for more information.

  • Both cursors and trees store a version number. If you modify the same tree with more than one cursor, you can get mismatched versions. If there is a mismatch, an exception is thrown.

  • If you allow duplicate keys, seek always returns the first key that matches. For example, the cursor will always match at the first instance of 'c': (a,b,*c,c,c,d,e).

EMBEDDING API

Flexibility is paramount. The embedding API is much more flexible than would be possible with C++ templates. See tvcommon.* & tv.*.

PERFORMANCE

  • Average Fill

    The number elements in the collection divided by the number of available slots. Higher is better. (Perl built-in hashes max out around 50-60%. Hash tables generally max out at around 70%.)

  • Average Depth

    The average number of nodes to be inspected during a search. Lower is better.

  • Average Centering

    Each fat-node is essentially an array of elements. This array is allocated contiguously from the available slots. The best arrangement (for insertions & deletions) is if the block of filled slots is centered.

REFERENCES

  • http://paris.lcs.mit.edu/~bvelez/std-colls/cacm/cacm-2455.html

    Author: Foster, C. C.

    A generalization of AVL trees is proposed in which imbalances up to (triangle shape) is a small integer. An experiment is performed to compare these trees with standard AVL trees and with balanced trees on the basis of mean retrieval time, of amount of restructuring expected, and on the worst case of retrieval time. It is shown that, by permitting imbalances of up to five units, the retrieval time is increased a small amount while the amount of restructuring required is decreased by a factor of ten. A few theoretical results are derived, including the correction of an earlier paper, and are duly compared with the experimental data. Reasonably good correspondence is found.

    CACM August, 1973

  • http://www.imada.ou.dk/~kslarsen/Papers/AVL.html

      AVL Trees with Relaxed Balance 
      Kim S. Larsen 
      Proceedings of the 8th International Parallel Processing Symposium,
      pp. 888-893, IEEE Computer Society Press, 1994. 

    AVL trees with relaxed balance were introduced with the aim of improving runtime performance by allowing a greater degree of concurrency. This is obtained by uncoupling updating from rebalancing. An additional benefit is that rebalancing can be controlled separately. In particular, it can be postponed completely or partially until after peak working hours.

    We define a new collection of rebalancing operations which allows for a significantly greater degree of concurrency than the original proposal. Additionally, in contrast to the original proposal, we prove the complexity of our algorithm. If N is the maximum size the tree could ever have, we prove that each insertion gives rise to at most floor(log_phi(N + 3/2) + log_phi(sqrt(5)) - 3) rebalancing operations and that each deletion gives rise to at most floor(log_phi(N + 3/2) + log_phi(sqrt(5)) - 4) rebalancing operations, where phi is the golden ratio.

PUBLIC SOURCE CODE

The source code is being released in a malleable form to encourage as much testing as possible. Bugs in fundemental collections are simply UNACCEPTABLE and it is hard to trust a single vendor to debug their code properly.

Get it via http://www.perl.com/CPAN/authors/id/JPRIT/ !

TODO

Optimize more!

Clean up refcnts in test scripts.

More documentation.

AUTHOR

Copyright © 1997-1999 Joshua Nathaniel Pritikin. All rights reserved.

This package is free software and is provided "as is" without express or implied warranty. It may be used, redistributed and/or modified under the terms of the Perl Artistic License (see http://www.perl.com/perl/misc/Artistic.html)

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