Dynamic Independent Set of Disks (and Hypercubes) Made Easier

Maintaining an approximate maximum independent set of a dynamic collection of objects has been studied extensively in the past few years. Recently, Bhore, Nöllenburg, Tóth, and Wulms (SoCG 2024) showed that for (unweighted) disks in the plane, it is possible to maintain O(1)-factor approximate solution in polylogarithmic amortized update time. In this work, we provide a much simpler dynamic O(1)-approximation algorithm, which at the same time improves the number of logarithmic factors in the previous update time bound. Along the way, we also obtain simpler and faster algorithms for dynamic independent set for axis-aligned hypercubes as well as static independent set for fat objects in any constant dimension. All the above results also hold for the minimum piercing set problem for the same classes of objects.