Labeling Downtown

Gabriele Neyerz and Frank Wagner x Abstract American cities, especially their central regions usually have a very regular street pattern: We are given a rectangular grid of streets, each street has to be labeled with a name running along its street, such that no two labels overlap. For this restricted but yet realistic case an e cient algorithmic solution for the generally hard labeling problem gets in reach. The main contribution of this paper is an algorithm that guarantees to solve every solvable instance. So far we are not able to provide a runtime analysis that guarantees e ciency, but the empirical behavior is polynomial without a single exception. The complexity status of the problem is open, we show that a slight generalization, namely the labeling of a cylinder shaped downtown, is NP-hard. Finally, we present e cient algorithms for three special cases including the case of having no labels that are more than half the length of their street.