Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, April 20, 2023, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Meghana M. Reddy

Local Complexity of Polygons and its Relevance in the Art Gallery Problem

Discrete and Computational Geometry often involve simple polygons or polygonal regions, with one of the classic problems being the Art Gallery Problem (AGP). However, many algorithms and data structures have significantly improved runtime if the underlying polygonal region has low local complexity. To provide a rigorous foundation for this notion, we present two possible formal definitions of local complexity of a polygon: point visibility width and chord visibility width. Additionally, we establish their combinatorial relationship. This is joint work with Fabian Klute and Tillmann Miltzow. Simon Hengeveld and Tillmann Miltzow have published an FPT algorithm for the AGP when parameterized by the chord visibility width, which we will briefly explore in our talk.

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