[whatwg] Question on Limits in Adaption Agency Algorithm
minamide at cs.tsukuba.ac.jp
Thu Aug 1 23:32:14 PDT 2013
On Mon, 1 Jul 2013, Ian Hickson wrote:
> One option would be to remove from the stack of open elements any
> elements that we are skipping when we bail out of the AAA.
> Can anyone see a problem with doing that?
I think that this solves the issue and clarifies the behaviour of
> The limits are really intended to reduce the memory consumption of the
> algorithm, not its running time. Elements are expensive, and this
> algorithm can create exponentially more elements than tags in the markup,
> when it's not limited.
Although I agree with the revision above, I would like to clarify
the behaviour of the AAA algorithm.
I don't think that the AAA algorithm can create exponentially more elements
even if it's not limited.
Let D be the depth of the stack of open elements and S the size of the DOM
tree that has been constructed so far.
Then after application of the algorithm:
* The size of the DOM tree is at most S + D.
* The depth of the stack of open elements is at most D.
Even if the algorithm is applied n times, the size of the DOM tree is bounded
by S + nD. (not S * 2^n)
In total, I think that the number of elements in the DOM tree is in
O(m^2) where m is the number of tags in the source HTML.
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