Semi-dynamic Connectivity in the Plane

  • Sergio CabelloEmail author
  • Michael Kerber
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9214)


Motivated by a path planning problem we consider the following procedure. Assume that we have two points s and t in the plane and take \(\mathcal {K}=\emptyset \). At each step we add to \(\mathcal {K}\) a compact convex set that is disjoint from s and t. We must recognize when the union of the sets in \(\mathcal {K}\) separates s and t, at which point the procedure terminates. We show how to add one set to \(\mathcal {K}\) in \(O(1+k\alpha (n))\) amortized time plus the time needed to find all sets of \(\mathcal {K}\) intersecting the newly added set, where n is the cardinality of \(\mathcal {K}\), k is the number of sets in \(\mathcal {K}\) intersecting the newly added set, and \(\alpha (\cdot )\) is the inverse of the Ackermann function.


Intersection Graph Adjacency List Path Planning Problem Polygonal Path Polygonal Curve 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Mathematics, IMFM, and Department of Mathematics, FMFUniversity of LjubljanaLjubljanaSlovenia
  2. 2.Max-Planck-Institut für InformatikSaarbrückenGermany

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