  In this paper, we develop a framework to obtain graph abstractions for
decision-making by an agent where the abstractions emerge as a function of the
agent's limited computational resources. We discuss the connection of the
proposed approach with information-theoretic signal compression, and formulate
a novel optimization problem to obtain tree-based abstractions as a function of
the agent's computational resources. The structural properties of the new
problem are discussed in detail, and two algorithmic approaches are proposed to
obtain solutions to this optimization problem. We discuss the quality of, and
prove relationships between, solutions obtained by the two proposed algorithms.
The framework is demonstrated to generate a hierarchy of abstractions for a
non-trivial environment.
