Improved bounds for the union of locally fat objects in the plane

Boris Aronov; Mark De Berg; Esther Ezrar; Micha Sharir

doi:10.1137/120891241

Improved bounds for the union of locally fat objects in the plane

Boris Aronov
, Mark De Berg
, Esther Ezrar
, Micha Sharir

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

Abstract

We show that, for any γ > 0, the combinatorial complexity of the union of n locally γ-fat objects of constant complexity in the plane is nγ4 2O(log n). For the special case of γ-fat triangles,the bound improves to O(n log n + n/γ log2 1/γ ).

Original language	English
Pages (from-to)	543-572
Number of pages	30
Journal	SIAM Journal on Computing
Volume	43
Issue number	2
DOIs	https://doi.org/10.1137/120891241
State	Published - 2014
Externally published	Yes

Keywords

Combinatorial geometry
Fat objects
Union complexity

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10.1137/120891241

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title = "Improved bounds for the union of locally fat objects in the plane",

abstract = "We show that, for any γ > 0, the combinatorial complexity of the union of n locally γ-fat objects of constant complexity in the plane is nγ4 2O(log n). For the special case of γ-fat triangles,the bound improves to O(n log n + n/γ log2 1/γ ).",

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AU - Ezrar, Esther

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AB - We show that, for any γ > 0, the combinatorial complexity of the union of n locally γ-fat objects of constant complexity in the plane is nγ4 2O(log n). For the special case of γ-fat triangles,the bound improves to O(n log n + n/γ log2 1/γ ).

KW - Combinatorial geometry

KW - Fat objects

KW - Union complexity

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Improved bounds for the union of locally fat objects in the plane

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Keywords

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