These interesting results agree with the findings of Lauscher and Reuter, who use an approach called Quantum Einstein Gravity, and with other recent theoretical work.
CDT theory uses a triangulation process which varies dynamically and follows deterministic rules, to map out how this can evolve into dimensional spaces similar to that of our universe.
CDT is a modification of quantum Regge calculus where spacetime is discretized by approximating it with a piecewise linear manifold in a process called triangulation.
In place of a smooth manifold there is a network of triangulation nodes, where space is locally flat (within each simplex) but globally curved, as with the individual faces and the overall surface of a geodesic dome.
CDT builds upon the earlier work of Barrett, Crane, and Baez, but by introducing the causality constraint as a fundamental rule (influencing the process from the very start), Loll, Ambjørn, and Jurkiewicz created something different.
The main difference between the two is that the causal set approach is relatively general, whereas CDT assumes a more specific relationship between the lattice of spacetime events and geometry.
Consequently, the Lagrangian of CDT is constrained by the initial assumptions to the extent that it can be written down explicitly and analyzed (see, for example, hep-th/0505154, page 5), whereas there is more freedom in how one might write down an action for causal-set theory.