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The Maximum Indpendent Set Problem in Unit Disk Graphs ∗

The class of intersection graphs of disks in the Euclidean plane, called disk graphs, was studied for many years for its theoretical aspects as well as for its applications. The maximum independent set problem on disk graphs (computing a largest subset of the given disks such that the disks in the subset are pairwise disjoint) has applications in map labeling. Under the assumption that labels occupy a circular area, the maximum number of non-intersecting labels that can be placed on a map (out of a given set of desired labels) is equal to the size of the maximum independent set in the corresponding disk graph.