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Date: Wed, 21 Feb 2001 23:32:04 +0100
From: Martin Mares <mj@suse.cz>
To: "H. Peter Anvin" <hpa@zytor.com>
Cc: linux-kernel@vger.kernel.org
Subject: Re: [rfc] Near-constant time directory index for Ext2
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Hello!

> Not true.  The rehashing is O(n) and it has to be performed O(log n)
> times during insertion.  Therefore, insertion is O(log n).

Rehashing is O(n), but the "n" is the _current_ number of items, not the
maximum one after all the insertions.

Let's assume you start with a single-entry hash table. You rehash for the
first time after inserting the first item (giving hash table of size 2),
then after the second item (=> size 4), then after the fourth item (=> size 8)
and so on. I.e., when you insert n items, the total cost of rehashing summed
over all the insertions is at most 1 + 2 + 4 + 8 + 16 + ... + 2^k (where
k=floor(log2(n))) <= 2^k+1 = O(n). That is O(1) operations per item inserted.

				Have a nice fortnight
-- 
Martin `MJ' Mares <mj@ucw.cz> <mj@suse.cz> http://atrey.karlin.mff.cuni.cz/~mj/
MIPS: Meaningless Indicator of Processor Speed.
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