The Internet is
surprisingly robust, and it remains connected on a global scale even
if a randomly chosen 99% of its connection points break down. However,
it is relatively fragile if its most highly connected points are selectively
knocked out. These are the conclusions of researchers applying physics
principles and precise mathematical models to the study of the worldwide
computer network.
The Internet consists
of computer networks (most commonly, "local area networks") connected
by various devices, known as routers and hubs. For simplicity's sake,
researchers consider each connection point as a generic "node." Previous
work suggests the fraction of Internet nodes having k connections is
proportional to k-a, for some number a. This is a "scale-free
power law distribution," which occurs commonly in nature and appears
in the frequency of earthquakes and the size distributions of clouds
and mountains.
Unlike an exponential
distribution, a scale-free power law distribution decays very slowly,
meaning in this case that there is a large proportion of computers that
still have a significant amount of connections. Recent computer simulations
of scale-free networks have shown that the Internet is resilient for
this reason (Albert et al., Nature, 27 July; Albert-Laszlo Barabasi,
Notre Dame, 219-631-5767, alb@nd.edu;
see also The Industrial Physicist, December 2000).
The latest work
now puts this conclusion on a firm mathematical footing. Two independent
groups (Reuven Cohen, Bar Ilan University, Israel, 011-972-8-9370131,
cohenr@shosji.ph.biu.ac.il;
Duncan Callaway, Cornell, 607-255-9174; dc52@cornell.edu)
apply percolation theory, developed by geophysicists interested in estimating
how much oil they could extract from reservoirs in a porous medium.
Percolation theory deals with systems containing points ("sites") and
connections between them, and it analyzes the behavior of the system
when one removes some of the sites or connections. Combined with the
insights from the scale-free distribution, the powerful percolation-based
approach may help Internet architects to maximize resistance against
Internet attacks, by controlling the distribution of nodes having certain
numbers of connections. (Cohen
et al, Phys. Rev. Lett, 20 Nov (Select Articles);
Callaway et al., Phys. Rev. Lett., upcoming.)
Back
to Physics News Update
