Lower Bounds for Kinetic Planar Subdivisions

We revisit the notion of kinetic efficiency for noncanonically defined discrete attributes of moving data, like binary space partitions and triangulations. Under reasonable computational models, we obtain lower bounds on the minimum amount of work required to maintain any binary space partition of moving segments in the plane or any Steiner triangulation of moving points in the plane. Such lower bounds—the first to be obtained in the kinetic context—are necessary to evaluate the efficiency of kinetic data structures when the attribute to be maintained is not canonically defined.

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