I saw the earlier fruitless discussion on the definition of "small world" networks.
Let me summarize my thoughts:
o You and Oskar may well be using the same definition.
o I suspect you have not read the papers you cite. The wikipedia article
is quite clear that small world networks are a subclass of random graphs. The
paper is talking about random rewirings. Oskar and you agreed the other day
that _all_ DHTs form small world networks. Something is amiss.
o Take some DHT, say CAN. It decidedly does not fit the 'definition' provided
by Watts and Strogatz.
o The definition provided by Watts and Strogatz is quite loose in the first place.
o I also question why, if 'small worlds' were such an important, fundamental,
defining characteristic of graphs, it took mankind until 1998 to come up
with a (catchy) name for them.
o I maintain that there is more hype here than substance.
But look, I don't _really_ care if you guys build systems with O(log^2 N) lookup
time when better techniques are available. It just so happens that too much
noise misplaced in an area will creat a fog and lead people astray. But hey, at
the end of the day, it's someone else's problem. I saw 40+ hop simulations and
felt the need to call it as I saw it.
Bob.
Oskar and I seem to be using the same definition of "small world
network", the same definition put forth by Watts and Strogatz when
they defined the term, also the same as the definition given in
Wikipedia, as well as in several books and peer-reviewed publications
devoted to the topic. (http://en.wikipedia.org/wiki/Small-world_network,
Watts, D. J. and S. H. Strogatz. 1998. "Collective dynamics of 'small-world' networks". Nature 393:440-42.
http://tam.cornell.edu/SS_nature_smallworld.pdf)
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