Optical technology offers simple interconnection schemes with
straightforward layouts that support complex logical
interconnection patterns. The Passive Optical Star (POS)
is often suggested as a platform for implementing the optical
network: Logically it offers an all-to-all broadcast capability.
Indeed, it seems to give a good support for intensive parallel
computations involving massive transfer of information and broadcast,
such as Video and Graphic applications.
We investigate the use of POS optical technology as the
communication medium for parallel computing.
In particular, a feature of parallel models which is extremely
important for the simplicity of algorithm design and program
portability is the scalability property or
self-simulation capability. It states that when a
computation achieves a certain speedup on a large machine with
many processors, then it achieves a similar speedup on any
smaller machine (relative to the number of processors).
We show that the POS is indeed scalable, namely, we present a
randomized algorithm for an n-processor n-wavelength POS
that does not assume global knowledge and that simulates a
kn-processor kn-wavelength POS with a slowdown of
O(k + \log ^* n). We then show how to route k-relations
on the n-processor POS in O(k \log^* n) steps, thus
proving that the power of broadcast incorporated in the POS
model may be applied to point-to-point communication problems
as well (there is a higher lower-bound for the point-to-point
n-processor OCPC).