The map labeling problem is a classical problem of cartography. There is a theoretically optimal approximation algorithm A. Unfortunately A is useless in practice as it typically produces results that are intolerably far off the optimal size. On the other hand there are heuristics with good practical results. In this paper we present an algorithm B that (1) guarantees the optimal approximation quality and runtime behaviour of A, and (2) yields results significantly closer to the optimum than the best heuristic known so far. The sample data used in the experimental evaluation consists of three different classes of random problems and a selection of problems arising in the production of groundwater quality maps by the authorities of the City of Munich.