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        <identifier>oai:drops-oai.dagstuhl.de:19990</identifier>
        <datestamp>2024-06-06T06:21:15Z</datestamp>
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          <dc:title>Sweeping Arrangements of Non-Piercing Regions in the Plane</dc:title>
          <dc:creator>Dalal, Suryendu</dc:creator>
          <dc:creator>Gangopadhyay, Rahul</dc:creator>
          <dc:creator>Raman, Rajiv</dc:creator>
          <dc:creator>Ray, Saurabh</dc:creator>
          <dc:subject>Sweeping</dc:subject>
          <dc:subject>Pseudodisks</dc:subject>
          <dc:subject>Discrete Geometry</dc:subject>
          <dc:subject>Topology</dc:subject>
          <dc:description>Let Γ be a finite set of Jordan curves in the plane. For any curve γ ∈ Γ, we denote the bounded region enclosed by γ as γ̃. We say that Γ is a non-piercing family if for any two curves α , β ∈ Γ, α̃ ⧵ β̃ is a connected region. A non-piercing family of curves generalizes a family of 2-intersecting curves in which each pair of curves intersect in at most two points. Snoeyink and Hershberger ("Sweeping Arrangements of Curves", SoCG '89) proved that if we are given a family Γ of 2-intersecting curves and a sweep curve γ ∈ Γ, then the arrangement can be swept by γ while always maintaining the 2-intersecting property of the curves. We generalize the result of Snoeyink and Hershberger to the setting of non-piercing curves. We show that given an arrangement of non-piercing curves Γ, and a sweep curve γ ∈ Γ, the arrangement can be swept by γ so that the arrangement remains non-piercing throughout the process. We also give a shorter and simpler proof of the result of Snoeyink and Hershberger, and give an eclectic set of applications.</dc:description>
          <dc:publisher>Schloss Dagstuhl – Leibniz-Zentrum für Informatik</dc:publisher>
          <dc:contributor>Suryendu Dalal and Rahul Gangopadhyay and Rajiv Raman and Saurabh Ray</dc:contributor>
          <dc:date>2024</dc:date>
          <dc:relation>Is Part Of LIPIcs, Volume 293, 40th International Symposium on Computational Geometry (SoCG 2024)</dc:relation>
          <dc:type>InProceedings</dc:type>
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          <dc:identifier>doi:10.4230/LIPIcs.SoCG.2024.45</dc:identifier>
          <dc:identifier>urn:nbn:de:0030-drops-199900</dc:identifier>
          <dc:identifier>https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.45</dc:identifier>
          <dc:language>eng</dc:language>
          <dc:rights>https://creativecommons.org/licenses/by/4.0/legalcode</dc:rights>
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