Browsing by Author "De Berg, Mark"

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    Computing Smallest Convex Intersecting Polygons
    (2022-09-01) Antoniadis, Antonios; De Berg, Mark; Kisfaludi-Bak, Sándor; Skarlatos, Antonis; Department of Computer Science; Chechik, Shiri; Navarro, Gonzalo; Rotenberg, Eva; Herman, Grzegorz; Professorship Kisfaludi-Bak Sándor; Computer Science Professors; Computer Science - Algorithms and Theoretical Computer Science (TCS); University of Twente; Eindhoven University of Technology; University of Salzburg
    A polygon C is an intersecting polygon for a set O of objects in R2 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.