I've structured a novel static interconnection topology for parallel and distributed a system which shows considerable advantages over existing static interconnection topologies in terms of its physical properties. Now I must support my novel topology with practical comparison. To do that how can I choose a practical problem and categorize the results?
This is a good question.
One way to make the comparison between a new topology and any other topology is to do the following:
1. Let your new topology be a set $\tau$ of points in some space $X$ that satisfy the union and intersection conditions for a topological space and guarantee that $\tau$ includes $X$ and the empty set.
2. Let $Y$ be another topology.
3. Endow $\tau$ and $Y$ with a proximity relation $\delta$ such as the Wallman proximity. Recall that the Wallman proximity satisfies the 4 Cech conditions for a proximity and the closure rule holds true. Let $\mbox{cl}A$ denote the closure of $A$. That is, for example, let $A,B\subset \tau$ and guarantee that $\delta$ satisfies the following condition:
\[
A \delta B\ \mbox{if and only if}\ \mbox{cl}A \cap \mbox{cl}B \neq \emptyset.
\[
4. Define a mapping $f$ on $\tau$ into $Y$ such that $f(A)\delta f(B)$, provided $A \delta B$.
This framework will make it possible to compare topologies.
This is a good question.
One way to make the comparison between a new topology and any other topology is to do the following:
1. Let your new topology be a set $\tau$ of points in some space $X$ that satisfy the union and intersection conditions for a topological space and guarantee that $\tau$ includes $X$ and the empty set.
2. Let $Y$ be another topology.
3. Endow $\tau$ and $Y$ with a proximity relation $\delta$ such as the Wallman proximity. Recall that the Wallman proximity satisfies the 4 Cech conditions for a proximity and the closure rule holds true. Let $\mbox{cl}A$ denote the closure of $A$. That is, for example, let $A,B\subset \tau$ and guarantee that $\delta$ satisfies the following condition:
\[
A \delta B\ \mbox{if and only if}\ \mbox{cl}A \cap \mbox{cl}B \neq \emptyset.
\[
4. Define a mapping $f$ on $\tau$ into $Y$ such that $f(A)\delta f(B)$, provided $A \delta B$.
This framework will make it possible to compare topologies.
Thank you so much professor for your valuable reply. Hope I'll follow the steps that you have given above and I would like to make my correspondence with you as permanent.
When comparing your topology with others that you are not so sure is a fairly comparison, try to use different traffic models like: random, bit reversal, shuffle, butterfly, transpose, etc. This can ensure that you are not overfitting your model even more when you are using static topologies.
In the results you can present the node utilization, packet conflicts and backlog of the messages. Shortest paths sometimes causes more conflicts for the same path than other routes that can avoid the use of same nodes, this increases considerably the throughput ot the system in different ways based upon the different traffic models.
Other factors to consider regarding routing in the IN from the implementation point of view:
How easy is to implement a deadlock-free routing function?. Could be extended to provide fault-tolerance?
If it uses routing tables, what is the cost of initialising them?
Does that routing function balances the load over the links?
Are there any pathological patterns?
Dear Cruz,
Thanks for your answer. There is no pathological patterns in my topology. But I've problem in programming it in nvidia using cuda programming. Can you suggest me a proper guidance in this regarding. Thanks
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