Analyze span - two parallel for

If I have an algorithm with two parallel for and I want to analyze the span of the algorithm, what do I have to do?

For example

parallel for a=2 to n
    parallel for 开发者_StackOverflowb=1 to a-1

My guess is the span is theta(lg(n)*lg(n)) but I'm not sure. :) Someone who can help or give a hint?

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I am assuming you want the time complexity of this algorithm. Since time complexity is NOT how much time the algorithm actually takes, but rather how much operations are needed for it [a quote supporting this claim follows], the time complexity of this algorithm is O(n^2), as it was if it was not parallel.

from the wiki page: Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, where an elementary operation takes a fixed amount of time to perform

Why don't we care for the fact the algorithm is parallel?
Usually, our cluster size is fixed, and does not depend on the input [n]. let the cluster size be k [meaning, we can perform k operations simultaneously and the algorithm is O(n^2) [for simplicity assume exactly n^2]
assume we have an input of size 100, then it will 'take' (100^2)/k time. if it was of size 1,000, it would take (1000^2)/k, and for n elements: (n^2)/k, as you can see, the k is a constant, and the fact that the program is parallel does not change the complexity. Being able to do k operations at once, is not better [and even worth, but that's for another thread] then a computer k time faster.