Subject: [manet] how to generate node positions following power law distribution?

From: "Yu" <[email-masked]>
Date: Tue, 31 Jan 2006 00:25:30 -0600

Hi,

I am trying to simulate a mobile network (within a rectangular area) where
nodes move around following power law distribution, i.e., a node moves to a
specific position A with probability c*(1/d)^m, where c and m are the
constant and exponent of the power law distribution, respectively. d is the
distance from position A to the node's initial location.

Currently I have two possible approaches to do this job. None of them is
perfect. In the first approach, the whole area is divided into small cells
so that I can calculate the probability that a node can drop in each cell.
Then a series of uniformly distributed random number can be used to
approximate the power law distribution. However, in order to obtain quality
approximation, the cell must be very small. Thus, the computation complexity
and the memory requirement can be extremly high, if the network size or node
number increase.

Another way is described here:
http://mathworld.wolfram.com/RandomNumber.html
Following this approach, I can get a series of random number following power
law distribution. This number, however, is actually the distance to a node's
initial location. How to locate a position using this distance is also a
problem since there are multiple positions (actually it may be multiple
curves) with the same distance. An intuitive way is to generate another
uniformly distributed random number B (for example, the angle) so that one
of the positions can be picked up. The problem is how to determing the
upper/lower bounds of this uniformly distributed random number B. This may
also dramatically increase the compexity.

There are also some articles discussing how to generate network with node's
out degree following power law distribution. I don't know if/how I can use
them for my purpose.

Does anyone know about any ready software package doing this job? I really
appreciate if you can share some useful information with me. Please also
kindly let me know if I have any misunderstanding.

Thanks,
Yu

----------------------------------------------
Yu Wang, Ph.D. Candidate
The Center for Advanced Computer Studis (CACS)
University of Louisiana at Lafayette, LA 70504
Website: http://www.louisiana.edu/~yxw1516/
Email: [email-masked]

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