On the union of κ-round objects in three and four dimensions

Boris Aronov, Alon Efrat, Vladlen Koltun, Micha Sharir

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

A compact set c in ℝd is κ-round if for every point p ∈ ∂ C there exists a closed ball that contains p, is contained in c, and has radius κ diam c. We show that, for any fixed κ > 0, the combinatorial complexity of the union of n κ-round, not necessarily convex, objects in ℝ3 (resp., in ℝ4) of constant description complexity is O(n2+ε) (resp., O(n 3+ε)) for any ε > 0, where the constant of proportionality depends on ε, κ, and the algebraic complexity of the objects. The bound is almost tight in the worst case.

Original languageEnglish (US)
Pages (from-to)511-526
Number of pages16
JournalDiscrete and Computational Geometry
Volume36
Issue number4
DOIs
StatePublished - 2006

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Union
Algebraic Complexity
Combinatorial Complexity
Compact Set
Ball
Radius
Closed
Object

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Discrete Mathematics and Combinatorics
  • Geometry and Topology

Cite this

On the union of κ-round objects in three and four dimensions. / Aronov, Boris; Efrat, Alon; Koltun, Vladlen; Sharir, Micha.

In: Discrete and Computational Geometry, Vol. 36, No. 4, 2006, p. 511-526.

Research output: Contribution to journalArticle

Aronov, Boris ; Efrat, Alon ; Koltun, Vladlen ; Sharir, Micha. / On the union of κ-round objects in three and four dimensions. In: Discrete and Computational Geometry. 2006 ; Vol. 36, No. 4. pp. 511-526.
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