Thoughts and request for guidance.

Sitaraman Vilayannur

  Hope this an appropriate group to broach this. 
  Is something along the below lines for the controller and management of SDN network and it open source implementation in the works...any pointers,  feedbacks/guidance is much appreciated.
 Thanks much.

Exploiting SDN Capabilities:

Some thoughts on the controller considerations for exploiting programmable networks with information centric or content based routing. 

 I was listening in to Stanfords Courseera course on PGM and Expander Graphs..and chanced upon Feynmans lectures where he was talking about the relationship to Mathematics and Physics where though Feynman hadnt mentioned  explicitly seemed to touch upon convexity and duality.... ..and attempted to relate this to SDN networks....

Duality between the algorithmic approach and the nature of the optimization problem.

                One convex algorithmic approach could be to resort to viewing the entire problem as a graph and optimize on the nature of such graph.

                One non-convex algorithmic approach could be a  Newton gradient method.

Decomposition of an overall optimization problem into non-convex subcomponents which subcomponents can be treated jointly as a convex problem.  Such decomposition method could be by determining components (Exapander components?) that are well connected.



Convexity could vary with the time window size of the problem.   At a given time instant or narrow time window, (routing) the problem is a convex one which one or a narrow set of optimum routing decisions, but due to changing traffic conditions, over a period of time individual routing decisions become a non-convex optimization problem. Therefore, an SDN control could possibly have non-convex (greedy?) approach component and a non-greedy component (viewing problem as a graph with expander subcomponets, each of which could in turn apply the greedy method).

When we bring time axis into the picture, the convexity of the problem changes from convex (short time window) to non-convex (large time window, to make decisions based on current and expected traffic pattern). Therefore the algorithmic approach to the control could change from  a non-convex (short time frame) to a convex (large time frame).  One way of doing this could be for the non-convex components to contribute weights (which determination could have a convex nature to it or at least partly determined by a convex component) to the elements of the convex components (a graph)

When one considers the Information based routing capability, ICN or advanced versions of the same. Here for a short time window, the placement of Information is a non-convex problem, and based on typical information demand, over a large time-window (placement and information content of caches ) could be considered a convex one.   Therefore, information superimposes an orthogonal nature on the convexity to the data component of the SDN-ICN combine.

Stochasticity and time window: While routing in any given network necessarily has to be deterministic, the optimal nature of the same introduces stochasticity amongst the possibly multiple options each of which individually yield deterministic routing. 

Here we would then need to consider the same issues as above wherein a general problem could be started off with a PGM and based on expander sections of this graph, now be decomposed into its non-convex (nature of the probabilistic problem) subcomponents.  It appears that information placement and routing could draw heavily on such PGM as semantic connectivity (again to be considered both across space and time as the vanilla version described above) could be probabilistic. Bringing in Content based Routing and Information Centric Routing therefore could be viewed as  bringing in a "placement" component to routing problem, eerily close but probably a lot more complex than what the VLSI folks deal with.  Therefore, the hardware folks probably have nothing to worry Software Defined Networks are going to use Hardware algorithms after all 

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