The complexity and construction of many faces in arrangements of lines and of segments
Edelsbrunner, Herbert
Guibas, Leonidas
Sharir, Micha
We show that the total number of edges ofm faces of an arrangement ofn lines in the plane isO(m 2/3– n 2/3+2 +n) for any>0. The proof takes an algorithmic approach, that is, we describe an algorithm for the calculation of thesem faces and derive the upper bound from the analysis of the algorithm. The algorithm uses randomization and its expected time complexity isO(m 2/3– n 2/3+2 logn+n logn logm). If instead of lines we have an arrangement ofn line segments, then the maximum number of edges ofm faces isO(m 2/3– n 2/3+2 +n (n) logm) for any>0, where(n) is the functional inverse of Ackermann's function. We give a (randomized) algorithm that produces these faces and takes expected timeO(m 2/3– n 2/3+2 log+n(n) log2 n logm).
Springer
1990
info:eu-repo/semantics/article
doc-type:article
text
http://purl.org/coar/resource_type/c_6501
https://research-explorer.app.ist.ac.at/record/4072
Edelsbrunner H, Guibas L, Sharir M. The complexity and construction of many faces in arrangements of lines and of segments. <i>Discrete & Computational Geometry</i>. 1990;5(1):161-196. doi:<a href="https://doi.org/10.1007/BF02187784">10.1007/BF02187784</a>
eng
info:eu-repo/semantics/altIdentifier/doi/10.1007/BF02187784
info:eu-repo/semantics/altIdentifier/issn/0179-5376
info:eu-repo/semantics/altIdentifier/issn/1432-0444
info:eu-repo/semantics/closedAccess