  In this paper, a mixed-integer linear programming formulation for the problem
of obtaining task-relevant, multi-resolution, graph abstractions for
resource-constrained agents is presented. The formulation leverages concepts
from information-theoretic signal compression, specifically the information
bottleneck (IB) method, to pose a graph abstraction problem as an optimal
encoder search over the space of multi-resolution trees. The abstractions
emerge in a task-relevant manner as a function of agent information-processing
constraints, and are not provided to the system a priori. We detail our
formulation and show how the problem can be realized as an integer linear
program. A non-trivial numerical example is presented to demonstrate the
utility in employing our approach to obtain hierarchical tree abstractions for
resource-limited agents.
