Robotics Research Technical Report, Vol. 255: The Complexity of Many Faces in Arrangements of Lines and of Segments (Classic Reprint) - Tapa dura

Sinopsis

Excerpt from Robotics Research Technical Report, Vol. 255: The Complexity of Many Faces in Arrangements of Lines and of Segments

In our present application, the desired upper bound on K(m,n) is obtained by analyz ing the space complexity of the resulting algorithm. The time complexity of the algo rithm is roughly a polylogarithmic factor times the upper bound on K(m,n) men tioned above (see Section 3 for a more precise bound). The algorithm is based on a random sampling technique akin to the e - net method of Haussler and Welzl [hw] and to the random sampling method of Clarkson [cl]. We obtain a randomized algorithm which always terminates and produces the desired output and which, with high pro bability, does so within the stated time bound.

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