Computing the L1 Geodesic Diameter and Center of a Simple Polygon in Linear Time

In this paper, we show that the L 1 geodesic diameter and center of a simple polygon can be computed in linear time. For the purpose, we focus on revealing basic geometric properties of the L 1 geodesic balls, that is, the metric balls with respect to the L 1 geodesic distance. More specifically, in this paper we show that any family of L 1 geodesic balls in any simple polygon has Helly number two, and the L 1 geodesic center consists of midpoints of shortest paths between diametral pairs. These properties are crucial for our linear-time algorithms, and do not hold for the Euclidean case.

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