MPI-INF/SWS Research Reports 1991-2021

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On the parallel complexity of degree sequence problems

Arikati, Srinivasa R.

November 1994, 12 pages.

Status: available - back from printing

We describe a robust and efficient implementation of the Bentley-Ottmann sweep line algorithm based on the LEDA library of efficient data types and algorithms. The program computes the planar graph $G$ induced by a set $S$ of straight line segments in the plane. The nodes of $G$ are all endpoints and all proper intersection points of segments in $S$. The edges of $G$ are the maximal relatively open subsegments of segments in $S$ that contain no node of $G$. All edges are directed from left to right or upwards. The algorithm runs in time $O((n+s) log n)$ where $n$ is the number of segments and $s$ is the number of vertices of the graph $G$. The implementation uses exact arithmetic for the reliable realization of the geometric primitives and it uses floating point filters to reduce the overhead of exact arithmetic.

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  AUTHOR = {Arikati, Srinivasa R.},
  TITLE = {On the parallel complexity of degree sequence problems},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-94-162},
  MONTH = {November},
  YEAR = {1994},
  ISSN = {0946-011X},