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

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