Consider a set of customers (e.g., WiFi receivers) and a set of service providers (e.g., wireless access points), where each provider has a capacity and the quality of service offered to its customers is anti-proportional to their distance. The capacity constrained assignment (CCA) is a matching between the two sets such that (i) each customer is assigned to at most one provider, (ii) every provider serves no more customers than its capacity, (iii) the maximum possible number of customers are served, and (iv) the sum of Euclidean distances within the assigned provider-customer pairs is minimized. Although max-flow algorithms are applicable to this problem, they require the complete distance-based bipartite graph between the customer and provider sets. For large spatial datasets, this graph is expensive to compute and it may be too large to fit in main memory. Motivated by this fact, we propose efficient algorithms for optimal assignment that employ novel edge-pruning strategies, based on the spatial properties of the problem. Additionally, we develop incremental techniques that maintain an optimal assignment (in the presence of updates) with a processing cost several times lower than CCA re-computation from scratch. Finally, we present approximate (i.e., suboptimal) CCA solutions that provide a tunable trade-off between result accuracy and computation cost, abiding by theoretical quality guarantees. A thorough experimental evaluation demonstrates the efficiency and practicality of the proposed techniques.