On 3/20/06, Bob Harris <[EMAIL PROTECTED]> wrote:
> ...
> Small worlds
> typically need O(log N) connections to other nodes to maintain
> connectivity. Pastry and Chord use O(log N) connections as well. Small
> worlds get O(log^2 N) hop lookups, Pastry and Chord get O(log N).
> Remind me how x^2 packets and x^2 processing is better than x.

there's a trade off here; what good is an O(log N) topology when it's
broken?  resilience is typically better in small worlds precisely
because they are unstructured.  directed/coordinated attacks against
highly structured networks are highly effective (not to mention the
usual intermittent failures, but most of these models assume a random
distribution of failure - this is an invitation to malicious intent)

also consider real world networks where such relationships /
topologies exist: in our wireless networks unidirectional links
present from a 30mW client in a coffee shop vary greatly from links
present on a high power amplified panel array mounted on a tower. 
this type of node disparity is more akin to small world than a highly
structured overlay.

and in practice you'll probably find yourself combining features of
both to make a resilient network that can function efficiently in good
conditions and remain functional in volatile / malicious environments.

just my $0.02
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