  In this work we introduce two novel deterministic annealing based clustering
algorithms to address the problem of Edge Controller Placement (ECP) in
wireless edge networks. These networks lie at the core of the fifth generation
(5G) wireless systems and beyond. These algorithms, ECP-LL and ECP-LB, address
the dominant leader-less and leader-based controller placement topologies and
have linear computational complexity in terms of network size, maximum number
of clusters and dimensionality of data. Each algorithm tries to place
controllers close to edge node clusters and not far away from other controllers
to maintain a reasonable balance between synchronization and delay costs. While
the ECP problem can be conveniently expressed as a multi-objective mixed
integer non-linear program (MINLP), our algorithms outperform state of art
MINLP solver, BARON both in terms of accuracy and speed. Our proposed
algorithms have the competitive edge of avoiding poor local minima through a
Shannon entropy term in the clustering objective function. Most ECP algorithms
are highly susceptible to poor local minima and greatly depend on
initialization.
