Smoothed Motion Complexity

We propose a new complexity measure for movement of objects, the smoothed motion complexity. Many applications are based on algorithms dealing with moving objects, but usually data of moving objects is inherently noisy due to measurement errors. Smoothed motion complexity considers this imprecise information and uses smoothed analysis [13] to model noisy data. The input is object to slight random perturbation and the smoothed complexity is the worst case expected complexity over all inputs w.r.t. the random noise. We think that the usually applied worst case analysis of algorithms dealing with moving objects, e.g., kinetic data structures, often does not reflect the real world behavior and that smoothed motion complexity is much better suited to estimate dynamics. We illustrate this approach on the problem of maintaining an orthogonal bounding box of a set of n points in Rd under linear motion. We assume speed vectors and initial positions from [−1, 1]d . The motion complexity is th...

• Type: Conference
• Year: 2003
• Where: ESA
• Authors: Valentina Damerow, Friedhelm Meyer auf der Heide, Harald Räcke, Christian Scheideler, Christian Sohler
• Keywords: Case Expected Complexity, ESA 2003, Smoothed Complexity, Smoothed Motion Complexity