Geometric permutations of non-overlapping unit balls revisited
نویسندگان
چکیده
منابع مشابه
Geometric permutations of balls with bounded size disparity
We study combinatorial bounds for geometric permutations of balls with bounded size disparity in d-space. Our main contribution is the following theorem: given a set S of n disjoint balls in R , if n is sufficiently large and the radius ratio between the largest and smallest balls of S is γ , then the maximum number of geometric permutations of S is O(γ logγ ). When d = 2, we are able to prove ...
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(i) We prove that the maximum number of geometric permutations, induced by line transversals to a collection of n pairwise disjoint balls in IR d , is (n d?1). This improves substantially the general upper bound of O(n 2d?2) given in 11]. (ii) We show that the maximum number of geometric permutations of a suuciently large collection of pairwise disjoint unit discs in the plane is 2, improving a...
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The touching graph of balls is a graph that admits a representation by non-intersecting balls in the space (of prescribed dimension), so that its edges correspond to touching pairs of balls. By a classical result of Koebe [?], the disc touching graphs are exactly the planar graphs. This paper deals with a recognition of unit-ball touching graphs. The 2– dimensional case was proved to be NP-hard...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2016
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2015.12.003