On 06/19/2012 02:18 PM, Mark Friedenbach wrote:
On Tue, Jun 19, 2012 at 10:33 AM, Alan Reiner <etothe...@gmail.com
<mailto:etothe...@gmail.com>> wrote:
If we were to use a raw trie structure, then we'd have all the above
issues solved: a trie has the same configuration no matter how
elements
are inserted or deleted, and accesses to elements in the tree are
constant time -- O(1). There is no such thing as an unbalanced trie.
But overall space-efficiency is an issue.
A PATRICIA tree/trie would be ideal, in my mind, as it also has a
completely deterministic structure, and is an order-of-magnitude more
space-efficient. Insert, delete and query times are still O(1).
However, it is not a trivial implementation. I have occasionally
looked
for implementations, but not found any that were satisfactory.
No, a trie of any sort is dependent upon distribution of input data
for balancing. As Peter Todd points out, a malicious actor could
construct transaction or address hashes in such a way as to grow some
segment of the trie in an unbalanced fashion. It's not much of an
attack, but in principle exploitable under particular timing-sensitive
circumstances.
Self-balancing search trees (KVL, RB, 2-3-4, whatever) don't suffer
from this problem.
Mark
I was using "unbalanced" to refer to "query time" (and also
insert/delete time). If your trie nodes branch based on the next byte
of your key hash, then the max depth of your trie is 32. Period. No
one can do anything to ever make you do more than 32 hops to
find/insert/delete your data. And if you're using a raw trie, you'll
always use /exactly/ 32 hops regardless of the distribution of the
underlying data. Hence, the trie structure is deterministic
(history-independent) and cannot become unbalanced in terms of access time.
My first concern was that a malicious actor could linearize parts of the
tree and cause access requests to take much longer than log(N) time.
With the trie, that's not only impossible, you're actually accessing in
O(1) time.
However, you are right that disk space can be affected by a malicious
actor. The more branching he can induce, the more branch nodes that are
created to support branches with only one leaf.
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