  Spatially correlated device activation is a typical feature of the Internet
of Things (IoT). This motivates the development of channel scheduling (CS)
methods that mitigate device collisions efficiently in such scenarios, which
constitutes the scope of this work. Specifically, we present a quadratic
program (QP) formulation for the CS problem considering the joint activation
probabilities among devices. This formulation allows the devices to
stochastically select the transmit channels, thus, leading to a soft-clustering
approach. We prove that the optimal QP solution can only be attained when it is
transformed into a hard-clustering problem, leading to a pure integer QP, which
we transform into a pure integer linear program (PILP). We leverage the
branch-and-cut (B&C) algorithm to solve PILP optimally. Due to the high
computational cost of B&C, we resort to some sub-optimal clustering methods
with low computational costs to tackle the clustering problem in CS. Our
findings demonstrate that the CS strategy, sourced from B&C, significantly
outperforms those derived from sub-optimal clustering methods, even amidst
increased device correlation.
