<div>Well actually, I don't want to figure out how to take advantage of a network topology, I want to figure out a clever weay for my optimization software to figure out how to take advantage of the topology. That is, I want my AI to solve the problem for me; my design for AI, is for the AI to figure out how to design itself.
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<div>So I look for problems that:</div>
<div>1. don't have obvious solutions from exisiting qualitative theory (e.g. genetic algorithms themselves; the best parameters, such as mutation rates, and selection of parameters, is still debated and the subject of experiments);
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<div>2. Can be interpreted by an algorithm (expressible in a finite representation, e.g. a network topology is a binary array, the question "what is the meaning of life?" is not so expressible)</div>
<div>3. the solution of the problem itself helps the method of solution; e.g., the optimization of a network topology, or the message passing system using a fixed topology, would itself improve the performance of the optimizing software running on the system; that is, the AI optimizes itself (indirectly).
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<div>So part of the reason I want a beowulf is that my AI can optimize it's platform, in the course of optimizing itself; besides being a horrible RAM hog and CPU hog and being trivially parallelizable (gen algs). So I"m interested in **any** topology that offers choices to running processes (should I call this distant idle node or that nearby busy node?) so it has something to optimize. So that's why hypercubes attract me. Besides it sounds all abstract mathy, even though it really isn't :-)
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<div>Peter<br><br> </div>
<div><span class="gmail_quote">On 5/23/07, <b class="gmail_sendername">Jim Lux</b> <<a href="mailto:James.P.Lux@jpl.nasa.gov">James.P.Lux@jpl.nasa.gov</a>> wrote:</span>
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<div><span class="q">At 09:19 AM 5/22/2007, Peter St. John wrote:<br>
<blockquote cite="http://" type="cite">A hypercube (<a onclick="return top.js.OpenExtLink(window,event,this)" href="http://en.wikipedia.org/wiki/Hypercube" target="_blank"> http://en.wikipedia.org/wiki/Hypercube</a>) also gets you exponential space; the max hops is the dimension (3 for a 3-dimensional cube) and the number of nodes is exp(base 2) of the dimension (8 vertices on a cube). To do a tesseract (4-cube), which looks like two cubes nested, you'd need 4 ports per node, 16 nodes, 32 cables, max hop 4. I've poked around and don't see a great 4 ports per node solution; I like the suggestion of putting a router on a motherboard.
</blockquote><br></span>Mind you, this is what Intel started with on their iPSC/1 and iPSC/2 computers. The early ones had multiple NICs in the nodes, then, later, they had a 8 port (I think) router in each node.<br><br>
It's not clear that this saves anything over a simpler architecture (e.g. external switch with lots of ports in a crossbar) unless you can do circuit switched routing (so you don't have a one packet delay in the switch) AND your algorithm can take advantage of it. I spent quite some time in the late 80s trying to figure out clever ways to take advantage of a hypercube topology for a modeling application.. I'm sure there are algorithms which are a natural fit, but the ones I was using weren't.
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<p>James Lux, P.E.<br>Spacecraft Radio Frequency Subsystems Group<br>Flight Communications Systems Section<br>Jet Propulsion Laboratory, Mail Stop 161-213<br>4800 Oak Grove Drive<br>Pasadena CA 91109<br>tel: (818)354-2075
<br>fax: (818)393-6875</p></div></blockquote></div><br>
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