Searching for the Kernel of a Polygon : A Competitive Strategy Using Self-Approaching Curves
We present a competitive strategy for walking into the kernel of an initially unknown star-shaped polygon. From an arbitrary start point, s, within the polygon, our strategy finds a path to the closest kernel point, k, whose length does not exceed 5:3331...times the distance from s to k. This is complemented by a general lower bound of v2. Our analysis relies on a result about a new and interesting class of curves which are self-approaching in the following sense. For any three consecutive points a, b, c on the curve the point b is closer to c than a to c. We show a tight upper bound of 5:3331... for the length of a self-approaching curve over the distance between its endpoints.
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