Recursive tilings and space-filling curves with little fragmentation

H.J. Haverkort

Recursive tilings and space-filling curves with little fragmentation

H.J. Haverkort

Algorithms

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic

Abstract

This paper defines the Arrwwid number of a recursive tiling (or space-filling curve) as the smallest number a such that any ball Q can be covered by a tiles (or curve fragments) with total volume O(volume(Q)). Recursive tilings and space-filling curves with low Arrwwid numbers may be applied to optimise disk, memory or server access patterns when processing sets of points in Rd. This paper presents recursive tilings and space-filling curves with optimal Arrwwid numbers. When d >= 3, regular cube tilings and space-??lling curves cannot have optimal Arrwwid number; alternatives with better Arrwwid numbers are presented.

Original language	English
Title of host publication	Abstracts 26th European Workshop on Computational Geometry (EuroCG 2010, Dortmund, Germany, March 22-24, 2010)
Editors	J. Vahrenhold
Place of Publication	Dortmund
Publisher	Technische Universität Dortmund
Pages	185-188
Publication status	Published - 2010
Event	26th European Workshop on Computational Geometry (EuroCG 2010) - Dortmund Duration: 22 Mar 2010 → 24 Mar 2010 Conference number: 26 http://eurocg.org/

Workshop

Workshop	26th European Workshop on Computational Geometry (EuroCG 2010)
Abbreviated title	EuroCG 2010
City	Dortmund
Period	22/03/10 → 24/03/10
Internet address	http://eurocg.org/

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title = "Recursive tilings and space-filling curves with little fragmentation",

abstract = "This paper defines the Arrwwid number of a recursive tiling (or space-filling curve) as the smallest number a such that any ball Q can be covered by a tiles (or curve fragments) with total volume O(volume(Q)). Recursive tilings and space-filling curves with low Arrwwid numbers may be applied to optimise disk, memory or server access patterns when processing sets of points in Rd. This paper presents recursive tilings and space-filling curves with optimal Arrwwid numbers. When d >= 3, regular cube tilings and space-??lling curves cannot have optimal Arrwwid number; alternatives with better Arrwwid numbers are presented.",

author = "H.J. Haverkort",

year = "2010",

language = "English",

pages = "185--188",

editor = "J. Vahrenhold",

booktitle = "Abstracts 26th European Workshop on Computational Geometry (EuroCG 2010, Dortmund, Germany, March 22-24, 2010)",

publisher = "Technische Universit{\"a}t Dortmund",

note = "26th European Workshop on Computational Geometry (EuroCG 2010), EuroCG 2010 ; Conference date: 22-03-2010 Through 24-03-2010",

url = "http://eurocg.org/",

}

Recursive tilings and space-filling curves with little fragmentation. / Haverkort, H.J.

Abstracts 26th European Workshop on Computational Geometry (EuroCG 2010, Dortmund, Germany, March 22-24, 2010). ed. / J. Vahrenhold. Dortmund : Technische Universität Dortmund, 2010. p. 185-188.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic

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N2 - This paper defines the Arrwwid number of a recursive tiling (or space-filling curve) as the smallest number a such that any ball Q can be covered by a tiles (or curve fragments) with total volume O(volume(Q)). Recursive tilings and space-filling curves with low Arrwwid numbers may be applied to optimise disk, memory or server access patterns when processing sets of points in Rd. This paper presents recursive tilings and space-filling curves with optimal Arrwwid numbers. When d >= 3, regular cube tilings and space-??lling curves cannot have optimal Arrwwid number; alternatives with better Arrwwid numbers are presented.

AB - This paper defines the Arrwwid number of a recursive tiling (or space-filling curve) as the smallest number a such that any ball Q can be covered by a tiles (or curve fragments) with total volume O(volume(Q)). Recursive tilings and space-filling curves with low Arrwwid numbers may be applied to optimise disk, memory or server access patterns when processing sets of points in Rd. This paper presents recursive tilings and space-filling curves with optimal Arrwwid numbers. When d >= 3, regular cube tilings and space-??lling curves cannot have optimal Arrwwid number; alternatives with better Arrwwid numbers are presented.

M3 - Conference contribution

SP - 185

EP - 188

BT - Abstracts 26th European Workshop on Computational Geometry (EuroCG 2010, Dortmund, Germany, March 22-24, 2010)

A2 - Vahrenhold, J.

PB - Technische Universität Dortmund

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T2 - 26th European Workshop on Computational Geometry (EuroCG 2010)

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