TY - JOUR
T1 - On levels in arrangements of lines, segments, planes, and triangles
AU - Agarwal, P. K.
AU - Aronov, B.
AU - Chan, T. M.
AU - Sharir, M.
PY - 1998/4
Y1 - 1998/4
N2 - We consider the problem of bounding the complexity of the kth level in an arrangement of n curves or surfaces, a problem dual to, and an extension of, the well-known k-set problem. Among other results, we prove a new bound, O(nk5/3), on the complexity of the kth level in an arrangement of n planes in ℝ3, or on the number of k-sets in a set of n points in three dimensions, and we show that the complexity of the kth level in an arrangement of n line segments in the plane is O(n-√kα(n/k)), and that the complexity of the kth level in an arrangement of n triangles in 3-space is O(n2k5/6α(n/k)).
AB - We consider the problem of bounding the complexity of the kth level in an arrangement of n curves or surfaces, a problem dual to, and an extension of, the well-known k-set problem. Among other results, we prove a new bound, O(nk5/3), on the complexity of the kth level in an arrangement of n planes in ℝ3, or on the number of k-sets in a set of n points in three dimensions, and we show that the complexity of the kth level in an arrangement of n line segments in the plane is O(n-√kα(n/k)), and that the complexity of the kth level in an arrangement of n triangles in 3-space is O(n2k5/6α(n/k)).
UR - http://www.scopus.com/inward/record.url?scp=0032372467&partnerID=8YFLogxK
U2 - 10.1007/PL00009348
DO - 10.1007/PL00009348
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:0032372467
SN - 0179-5376
VL - 19
SP - 315
EP - 331
JO - Discrete and Computational Geometry
JF - Discrete and Computational Geometry
IS - 3
ER -