Cutting Polygons into Small Pieces with Chords: Laser-Based Localization Esther M. Arkin Rathish Das Stony Brook University, NY, USA Stony Brook University, NY, USA
[email protected] [email protected] Jie Gao Mayank Goswami Rutgers University, Piscataway, NJ, USA Queens College of CUNY, New York, NY, USA
[email protected] [email protected] Joseph S. B. Mitchell Valentin Polishchuk Stony Brook University, NY, USA Linköping University, Norrköping, Sweden
[email protected] [email protected] Csaba D. Tóth California State University Northridge, Los Angeles, CA, USA Tufts University, Medford, MA, USA
[email protected] Abstract Motivated by indoor localization by tripwire lasers, we study the problem of cutting a polygon into small-size pieces, using the chords of the polygon. Several versions are considered, depending on the definition of the “size” of a piece. In particular, we consider the area, the diameter, and the radius of the largest inscribed circle as a measure of the size of a piece. We also consider different objectives, either minimizing the maximum size of a piece for a given number of chords, or minimizing the number of chords that achieve a given size threshold for the pieces. We give hardness results for polygons with holes and approximation algorithms for multiple variants of the problem. 2012 ACM Subject Classification Theory of computation → Approximation algorithms analysis; Theory of computation → Packing and covering problems; Mathematics of computing → Combinat- orial algorithms; Theory of computation → Computational geometry Keywords and phrases Polygon partition, Arrangements, Visibility, Localization Digital Object Identifier 10.4230/LIPIcs.ESA.2020.7 Related Version A full version of the paper is available at https://arxiv.org/abs/2006.15089.