Existing approaches to solving combinatorial optimization problems on graphs suffer from the need to engineer each problem algorithmically, with practical problems recurring in many instances. The practical side of theoretical computer science, such as computational complexity, then needs to be addressed. Relevant developments in machine learning research on graphs are surveyed for this purpose. We organize and compare the structures involved with learning to solve combinatorial optimization problems, with a special eye on the telecommunications domain and its continuous development of live and research networks.

Current trends strongly indicate a transition towards large-scale programmable networks with virtual network functions. In such a setting, deployment of distributed control planes will be vital for guaranteed service availability and performance. Moreover, deployment strategies need to be completed quickly in order to respond flexibly to varying network conditions. We propose an effective optimization approach that automatically decides on the needed number of controllers, their locations, control regions, and traffic routes into a plan which fulfills control flow reliability and routability requirements, including bandwidth and delay bounds. The approach is also fast: the algorithms for bandwidth and delay bounds can reduce the running time at the level of 50x and 500x, respectively, compared to state-of-the-art and direct solvers such as CPLEX. Altogether, our results indicate that computing a deployment plan adhering to predetermined performance requirements over network topologies of various sizes can be produced in seconds and minutes, rather than hours and days. Such fast allocation of resources that guarantees reliable connectivity and service quality is fundamental for elastic and efficient use of network resources. INDEX TERMS Software-defined networking, distributed control plane, controller placement problem, latency, reliability, routability, optimization. V K possible ways to map them on the network. For each mapping, there are K V possible ways of defining control regions.

Recent control plane solutions in a software-defined network (SDN) setting assume physically distributed but logically centralized control instances: a distributed control plane (DCP). As networks become more heterogeneous with increasing amount and diversity of network resources, DCP deployment strategies must be both fast and flexible to cope with varying network conditions whilst fulfilling constraints. However, current approaches are slow and only focus on controller placement, sometimes in combination with bandwidth or delay constraints. We demonstrate the capabilities of our optimization framework [1]-[3] for fast deployment of DCPs, emphasizing control service reliability, bandwidth and latency requirements. We show that the approach can produce robust deployment plans under changing network conditions. Compared to state of the art solvers, our approach is magnitudes faster, enabling fast DCP deployment within minutes and seconds rather than days and hours.