Re: Analysis for Linux-2.5 fix/improve get_pid(), comparing various approaches

[Andries Brouwer <aebr@win.tue.nl>]

On Fri, Aug 09, 2002 at 07:22:08AM -0400, Hubertus Franke wrote:

> Particulary for large number of tasks, this can lead to frequent exercise of
> the repeat resulting in a O(N^2) algorithm. We call this : <algo-0>.

Your math is flawed. The O(N^2) happens only when the name space for pid's
has the same order of magnitude as the number N of processes.
Now consider N=100000 with 31-bit name space. In a series of
2.10^9 forks you have to do the loop fewer than N times and
N^2 / 2.10^9 = 5. You see that on average for each fork there
are 5 comparisons.
For N=1000000 you rearrange the task list as I described yesterday
so that each loop takes time sqrt(N), and altogether N.sqrt(N)
comparisons are needed in a series of 2.10^9 forks.
That is 0.5 comparisons per fork.

You see that thanks to the large pid space things get really
efficient. Ugly constructions are only needed when a large fraction
of all possible pids is actually in use, or when you need hard
real time guarantees.

Andries