TY - JOUR
AB - We show that the maximum number of edges bounding m faces in an arrangement of n line segments in the plane is O(m2/3n2/3+nα(n)+nlog m). This improves a previous upper bound of Edelsbrunner et al. [5] and almost matches the best known lower bound which is Ω(m2/3n2/3+nα(n)). In addition, we show that the number of edges bounding any m faces in an arrangement of n line segments with a total of t intersecting pairs is O(m2/3t1/3+nα(t/n)+nmin{log m,log t/n}), almost matching the lower bound of Ω(m2/3t1/3+nα(t/n)) demonstrated in this paper.
AU - Aronov, Boris
AU - Herbert Edelsbrunner
AU - Guibas, Leonidas J
AU - Sharir, Micha
ID - 4053
IS - 3
JF - Combinatorica
TI - The number of edges of many faces in a line segment arrangement
VL - 12
ER -