The paradigm of shared spectrum allows secondary devices to opportunistically access spectrum bands underutilized by primary owners. Recently, the FCC has targeted the sharing of the 3.5 GHz (3550-3700 MHz) federal spectrum with commercial systems such as small cells. The rules require a spectrum access system (SAS) to accommodate three service tiers: 1) incumbent access; 2) priority access (PA); and 3) generalized authorized access (GAA). In this paper, we study the SAS-assisted dynamic channel assignment (CA) for PA and GAA tiers. We introduce the node-channel-pair conflict graph to capture pairwise interference, channel and geographic contiguity constraints, spatially varying channel availability, and coexistence awareness. The proposed graph representation allows us to formulate PA CA and GAA CA with binary conflicts as max-cardinality and max-reward CA, respectively. Approximate solutions can be found by a heuristic-based algorithm that searches for the maximum weighted independent set. We further formulate GAA CA with non-binary conflicts as max-utility CA. We show that the utility function is submodular, and the problem is an instance of matroid-constrained submodular maximization. A local-search-based polynomial-time algorithm is proposed which provides a provable performance guarantee. Extensive simulations using a real-world Wi-Fi hotspot location data set are performed to evaluate the proposed algorithms. Our results have demonstrated the advantages of the proposed graph representation and improved performance of the proposed algorithms over the baseline algorithms.