Dear All, A while ago I posted a question about augmented trees: http://thread.gmane.org/gmane.comp.lib.boost.devel/235004 There has also been other discussion recently in this thread: http://thread.gmane.org/gmane.comp.lib.boost.devel/236103 Unfortunately I have been manically bug-hunting for the last few weeks [*] and wasn't able to follow-up properly until now. Here are my thoughts: I'm aware of 3 applications for augmented trees: - O(log N) indexing, insertion and deletion; "best of list and vector" (i.e. Countertree). - Similar where the "value" of each node is variable, so one can accumulate over any range in O(log N) time (i.e. stl_ext_adv). - Interval trees. In the first two cases, the augmented value is the sum of the augmented values in the sub-nodes. In the last case, it's the maximum of them. Is anyone aware of any other applications that are not not very similar to those, e.g. where the augmentation is some other function of the sub-nodes? Question: with only three (or two, if the first is considered a special case of the second) different kinds of augmentation, is it worthwhile to try to distil out a generic augmented tree? Here is an interesting augmented tree implementation that attempts to be generic: http://kaba.hilvi.org/pastel/pastel/sys/redblacktree.htm This seems to work by exposing the tree structure in the iterator (i.e. the iterator has parent(), left() and right() methods that return other iterators), and by requiring a Customization class that is called to updated augmented data in a node when its children change. This looks to me to be a sensible approach, but I'm still not sure that it's better than just copy-and-paste when there are only two (or three) useful ways to apply it. Thoughts anyone? Regards, Phil. [*] My recent bug-hunting has really made me value the ease of working with open-source code like Boost. What might take 5 minutes with grep instead takes weeks of back-and-forth with "technical support" (or reverse-engineering with a disassembler) - literally 3 orders of magnitude less efficient.
On Wed, Nov 28, 2012 at 3:52 AM, Phil Endecott < spam_from_boost_dev@chezphil.org> wrote:
Dear All,
A while ago I posted a question about augmented trees:
There has also been other discussion recently in this thread:
Unfortunately I have been manically bug-hunting for the last few weeks [*] and wasn't able to follow-up properly until now. Here are my thoughts:
I'm aware of 3 applications for augmented trees: - O(log N) indexing, insertion and deletion; "best of list and vector" (i.e. Countertree). - Similar where the "value" of each node is variable, so one can accumulate over any range in O(log N) time (i.e. stl_ext_adv). - Interval trees.
This list does not include R-trees suggested by Adam Wulkiewicz. In the general case this is the best choice, since these trees work with both two and one dimensional extension rectangles. Only if you are sure that one dimensional extension intervals are sufficient for the problem you can use one of the listed data structures or containers. However, if some time later the problem becomes two dimensional the solution can not be fixed by adding another container for y-coordinate. This approach is not optimal. For the best performance you will need to re-implement the solution using R-trees.
Here is an interesting augmented tree implementation that attempts to be generic:
This seems to work by exposing the tree structure in the iterator (i.e. the iterator has parent(), left() and right() methods that return other iterators), and by requiring a Customization class that is called to updated augmented data in a node when its children change.
These trees provide facilities and extensions of STL containers similar to Countertree and augmented B+ trees. They do not offer efficient logarithmic time join and split operations. Note also, that the author says that this project is mostly for educational purposes. Regards, Vadim Stadnik
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Phil Endecott -
Vadim Stadnik