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

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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 -