Brian, > > Where I have N source addresses and M > > destination addresses, this is easily shown to be > > O(N*M). > > Well, not quite, if you have an address selection algorithm > that excludes some combinations up front.
With all due respect, what I said holds. I wasn't talking
about optimizations, engineering considerations, or other
constants (which I know you understand is what the
notation I used is intended to convey). Its O(N^2), just
like pairwise anything.
> Also, do we expect
> N or M to be >3 in many cases, or even >2 in most cases?
> So I think the practical value will be less than you fear,
> typically 4, and >9 would be very rare. Not that this is
> negligible, but it's not unthinkable either.
Ok, you say > 9 is rare, and maybe that's true, I have no
clue. Sitting here today if each address represented an
ISP, then it does seem like greater than some number
would be rare (I would think 5 or so; who has 5 ISPs
today?)
BTW, can you support your assertion that > 9 is rare in
any way?.
So the problem is this: We say that > 9 is very
rare. But suppose its not, and you and your correspondent
both have 10 ISPs, or some combination of your ISPs gives
you 10 addresses (10 makes for easy arithmetic, and is
one more than your number [9]). In this case M=10 and
N=10, and if you take the typical TCP timeout (3 sec in
every *nix I have access to), then it takes
(10*10*3)/60 = 5 minutes to determine that the host
isn't reachable. Today a host can do the same thing in
about 30 seconds.
So yes, there are engineering assumptions that can be
made, but the calculation still holds. That is the
problem, not the list of all things that could go right.
Dave
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