Design of network control algorithms to keep pace with developments
Network control (NC) algorithms are used to operate the networks that fuel today’s information society – one example being the routing of packets on the internet. However, designing these algorithms is becoming more challenging as network architectures become more complex and related services more diverse. Undertaken with the support of the Marie Skłodowska-Curie Actions (MSCA) programme, the FANC project has developed a new theoretical framework to accelerate the development of NC algorithms. “The new framework is based on gradient-descent-type methods (a class of algorithms widely used in many fields, including machine learning) where we replace the (exact) gradients with approximate gradients,” explains Victor Valls, project coordinator.
Approximation and adaptation make for better problem solving
As the framework’s key component, the gradient approximations allow to model problem features and advance algorithm variants that cover the needs of real-world applications. The algorithms are available in a Julia software package. Users only need to compute gradients that capture the features of their applications and meet an algorithmic-specific criterion (which the package provides) to ensure convergence. Valls notes the significance of this development lies in removing “the need to (re)design an entire algorithm from scratch for every application. Adapting the gradients of well-established numerical methods is enough.”
A new theory for new problems
“During the project, we revisited existing applications to illustrate the power of the new framework (e.g. data analytics problems), but we also applied our results to solve new problems that were not possible before.” Here, Valls is referring to Birkhoff and quantum switching applications. The first has to do with sparse decomposition of doubly stochastic matrices, a classical combinatorial problem studied by Birkhoff in 1946. The second consists of operating a quantum switch to distribute entanglements (e.g. entangled qubits), which is problematic due to the volatility of their connectivity with the clients. Using the new framework, FANC showed that Birkhoff’s algorithm can be regarded as a special case of gradient-descent – “and we could characterise, for the first time, the speed of Birkhoff’s algorithm,” Valls highlights. The results of this work, published in IEEE/ACM Transactions on Networking, enable the design of scheduling policies for communication systems that may be unable to use queues – that is, optical and quantum networks. The specific software package is available here. For quantum switching, Valls says: “We used the framework to characterise the capacity region of a quantum switch (in the presence of decoherence and memory constraints) and design gradient-based algorithms that can maximise the entanglement distribution. The problem is important as quantum switches will be one of the core components of the quantum internet.” True to form, this MSCA project also delivered on the topic of ‘Nurturing excellence by means of cross-border and cross-sector mobility’. During FANC, Valls collaborated with IBM Research New York. Now he is conducting research at IBM Research Dublin. Here, one of his current interests is using quantum networks to enable distributed quantum computing. “The outcomes of FANC will play a critical role in designing such algorithms,” Valls concludes.
Keywords
FANC, algorithm, network control, Birkhoff, quantum switching, quantum network, congestion control, gradient approximations
