Bounds on the length of convex partitions of polygons

  • Christos Levcopoulos
  • Andrzej Lingas
Session 5 VLSI
Part of the Lecture Notes in Computer Science book series (LNCS, volume 181)


A heuristic for partitioning rectilinear polygons into rectangles, and polygons into convex parts by drawing lines of minimum total length is proposed. For the input polygon with n vertices, k concave vertices and the perimeter of length p, the heuristic draws partitioning lines of total length O(plogk) and runs in time O(nlogn). To demonstrate that the heuristic comes close to optimal in the worst case, a uniform family of rectilinear polygons Qk with k concave vertices, k=1, 2, ... and a uniform family of polygons Pk with k concave vertices, k=1, 2, ... are constructed such that any rectangular partition of Qk has (total line) length Ω(plogk), and any convex partition of Pk has length Ω(plogk/loglogk). Finally, a generalization of the heuristic for minimum length of convex partition of simple polygons to include polygons with polygonal holes is given.


Directed Edge Simple Polygon Convex Part Recursion Tree Chain Versus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Christos Levcopoulos
    • 1
  • Andrzej Lingas
    • 1
  1. 1.The Department of Computer and Information ScienceLinköping UniversityLinköpingSweden

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