An efficient and effective approximation algorithm for the Map Labeling Problem

Abstract

The Map Labeling Problem is a classical problem of cartography. There is an approximation algorithm A which is theoretically optimal: A has optimal running time and guarantees a label size of 50 percent of the maximum. Unfortunately A is useless in practice as it typically produces results that are intolerably far off the optimal size. On the other hand there is a heuristic with good practical results, which is used in real applications.

Recently a hybrid algorithm was suggested that first runs A and then uses its result to control the heuristic.

In this paper we integrate the two parts of the hybrid method into an efficient and effective approximation algorithm. In addition we include a strategy to improve the empirical quality of the results significantly. The resulting algorithm B

• guarantees optimal approximation quality and runtime behaviour, and

• yields results 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 München.

This work was done at the Institut für Informatik, Fachbereich Mathematik und Informatik, Freie Universität Berlin, Takustraße 9, 14195 Berlin-Dahlem, Germany. It was supported by the ESPRIT BRA Project ALCOM II