Before revision:  We study the maximal independent set (MIS) and maximum independent set ( MAX-IS ) problems on dynamic sets of O(n) axis-parallel rectangles, which can be modeled as dynamic rectangle intersection graphs.
After revision: Map labeling is a classical problem in cartography and geographic information systems that asks to place labels for area, line, and point features, with the goal to select and place the maximum number of independent, i.e., overlap-free, labels. A practically interesting case is point labeling with axis-parallel rectangular labels of common size. In a fully dynamic setting, at each time step, either a new label appears or an existing label disappears. Then, the challenge is to maintain a maximum cardinality subset of pairwise independent labels with sub-linear update time. We study the maximal independent set (MIS) and maximum independent set ( MAX-IS ) problems on dynamic sets of O(n) axis-parallel rectangles, which can be modeled as dynamic rectangle intersection graphs.