The complexity of the union of (α,β)-covered objects

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

An (α, β)-covered object is a simply connected planar region c with the property that for each point p ∈ ∂c there exists a triangle contained in c and having p as a vertex, such that all its angles are at least α > 0 and all its edges are at least β.diam(c)-long. This notion extends that of fat convex objects. We show that the combinatorial complexity of the union of n (α, β)-covered objects of "constant description complexity" is O(λ s+2(n) log 2 n log log n), where s is the maximum number of intersections between the boundaries of any pair of given objects, and λ s (n) denotes the maximum length of an (n, s)-Davenport-Schinzel sequence. Our result extends and improves previous results concerning convex α-fat objects.

Original languageEnglish (US)
Pages (from-to)775-787
Number of pages13
JournalSIAM Journal on Computing
Volume34
Issue number4
DOIs
StatePublished - 2005

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Oils and fats
Union
Fat Objects
Combinatorial Complexity
Triangle
Intersection
Denote
Angle
Object
Vertex of a graph

Keywords

  • Fat objects
  • Motion planning
  • Realistic input models

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

The complexity of the union of (α,β)-covered objects. / Efrat, Alon.

In: SIAM Journal on Computing, Vol. 34, No. 4, 2005, p. 775-787.

Research output: Contribution to journalArticle

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