volume 34, issue 1, P11-24 2005
DOI: 10.1007/s00454-005-1165-3
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Abstract: We give a surprisingly short proof that in any planar arrangement of n curves where each pair intersects at most a fixed number (s) of times, the k-level has subquadratic (O(n 2−1/2s )) complexity. This answers one of the main open problems from the author's previous paper [Discrete Comput. Geom., 29:375-393, 2003], which provided a weaker upper bound for a restricted class of curves only (graphs of degree-s polynomials). When combined with existing tools (cutting curves, sampling, etc.), the new idea generat…

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