Computing Smallest Convex Intersecting Polygons
Abstract
A polygon C is an intersecting polygon for a set O of objects in the plane if C intersects each object in O, where the polygon includes its interior. We study the problem of computing the minimum-perimeter intersecting polygon and the minimum-area convex intersecting polygon for a given set O of objects. We present an FPTAS for both problems for the case where O is a set of possibly intersecting convex polygons in the plane of total complexity n. Furthermore, we present an exact polynomial-time algorithm for the minimum-perimeter intersecting polygon for the case where O is a set of n possibly intersecting segments in the plane. So far, polynomial-time exact algorithms were only known for the minimum perimeter intersecting polygon of lines or of disjoint segments.
Cite
@article{arxiv.2208.07567,
title = {Computing Smallest Convex Intersecting Polygons},
author = {Antonios Antoniadis and Mark de Berg and Sándor Kisfaludi-Bak and Antonis Skarlatos},
journal= {arXiv preprint arXiv:2208.07567},
year = {2022}
}
Comments
Accepted to ESA 2022