The explosion of data available in life sciences is fueling an increasing demand for expressive models and computational methods. Graph transformation is a model for dynamic systems with a large variety of applications. We introduce a novel method of the graph transformation model construction, combining generative and dynamical viewpoints to give a fully automated data-driven model inference method. The method takes the input dynamical properties, given as a "snapshot" of the dynamics encoded by explicit transitions, and constructs a compatible model. The obtained model is guaranteed to be minimal, thus framing the approach as model compression (from a set of transitions into a set of rules). The compression is permissive to a lossy case, where the constructed model is allowed to exhibit behavior outside of the input transitions, thus suggesting a completion of the input dynamics. The task of graph transformation model inference is naturally highly challenging due to the combinatorics involved. We tackle the exponential explosion by proposing a heuristically minimal translation of the task into a well-established problem, set cover, for which highly optimized solutions exist. We further showcase how our results relate to Kolmogorov complexity expressed in terms of graph transformation.

Modern network architectures, such as wireless sensor networks and cluster-based communication systems, demand a seamless integration of robust local connectivity with reliable global interconnectivity. In this paper, we model such layered networks via the Cartesian product Fm□Kn. The friendship graph Fm, formed by joining m triangles at a common vertex, captures the localized, hub-and-spoke clustering with enhanced local interconnectivity, beyond what a star graph can offer, and the complete graph Kn represents a uniformly interconnected backbone linking these clusters. In this setting, landmarks (or resolving sets) are crucial as they uniquely identify every node based solely on its distances to a carefully chosen subset of reference nodes, thereby facilitating efficient routing, localization, and fault detection.We establish exact values for the metric dimension of Fm□Kn for any parameter regime, thereby providing direct insights into the optimal selection of resolving sets for such architectures. Specifically, we prove that if (Formula presented), then (Formula presented), and if (Formula presented), then (Formula presented). For the intermediate case, (Formula presented), we develop a refined analysis by first deriving structural properties of metric bases and then formulating an optimization problem whose solution yields the desired metric dimension. In particular, for the intermediate regime (Formula presented), with (m, n) ≠ (3, 4), we obtain the exact value (Formula presented) .All our proofs are constructive across all parameter regimes. Moreover, we give linear-time constructions of metric bases in all regimes and a backbone-assisted distributed rollout that uses O(n) backbone messages and O(|W|) local notifications. These results support layered/clustered network designs, including wireless sensor networks (WSNs) and backbone topologies, and provide explicit formulas and minimal-landmark constructions, together with corresponding bounds on control traffic and per-node state, for clustered backbone architectures modeled by Fm□Kn.