About symmetric rank-1 random matrices

Optimized component supply in a graph with restricted node capability Answer

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Optimized component supply in a graph with restricted node capability

I’m a newbie in Graph concept and I’ve the next drawback:

I’ve a graph of $N$ nodes, that every one are occupied by ${m_i}_{i=1}^{N}$
components and have a capability (maximal occupancy) of ${Omega_{i=1}^{N}}$.

Now, the nodes attempt to dispatch some of their components to another nodes in line with a desk $Lambda$. I say “try” right here, as a result of they’re solely allowed to dispatch the weather so long as the maximal occupancy of the receiver is just not exceeded.
Otherwise, the weather exceeding the capability are dispatch advocate.

I’m to grasp, what the maximal variety of efficiently delivered components is.

My drawback is the next: If I initiate sequentially with one node and dispatch its components to all of the receivers, the maximal occupancy energy breathe exceeded, however they’re too gifting away components, such that no drawback happens.

At some level, this energy crack, as a result of plane with gifting away its outgoing components, one node’s capability is exceeded due to too many incoming packages.

The packages could not breathe misplaced, therefore they’re despatched advocate to the sender, which once more energy has to dispatch advocate some packages, such that its capability is just not exceeded. This energy result in a succession of different exceeding-problems and I’ve to rectify all these issues by “back-tracing” every sole packages path.

Is there an answer to the query, what number of packages every node (and this quantity could breathe scowl than their scheduled sendings) could dispatch in organize to not transcend any nodes capability whereas optimizing the variety of completely efficiently delivered packages?

Is there a arm of Graph concept coping with these supply issues?

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