Searching for the Kernel of a Polygon - A Competitive Strategy

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 √ 2. 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. Keywords. Competitive strategy, on-line strategy, simple polygon, kernel, curves with increasing chords, self-approaching curves, geometric optimization.

• Type: Conference
• Year: 1995
• Where: COMPGEOM
• Authors: Christian Icking, Rolf Klein
• Keywords: Closest Kernel Point, Competitive Strategy, COMPGEOM 1995, Discrete Geometry, Unknown Star-shaped Polygon