Voronoi diagrams of rigidly moving sets of points

Daniel P. Huttenlocher; Klara Kedem; Jon M. Kleinberg

doi:10.1016/0020-0190(92)90204-9

Voronoi diagrams of rigidly moving sets of points

Daniel P. Huttenlocher
, Klara Kedem
, Jon M. Kleinberg

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

9 Scopus citations

Abstract

Consider k sets each consisting of n points in the plane, with each set allowed to move rigidly according to some continuous function of time. A paper by Aonuma, Imai, Imai, and Tokuyama shows an upper bound of O(n³k⁴log^*n) on the number of combinatorial changes to the Voronoi diagram of the kn points over all time. We present a bound of O(n²k²λ_s(k)) for s fixed s, thus improving their result by slightly more than a factor of kn.

Original language	English
Pages (from-to)	217-223
Number of pages	7
Journal	Information Processing Letters
Volume	43
Issue number	4
DOIs	https://doi.org/10.1016/0020-0190(92)90204-9
State	Published - 28 Sep 1992
Externally published	Yes

Keywords

Analysis of algorithms
Voronoi diagrams
computational geometry

ASJC Scopus subject areas

Theoretical Computer Science
Signal Processing
Information Systems
Computer Science Applications

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10.1016/0020-0190(92)90204-9

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title = "Voronoi diagrams of rigidly moving sets of points",

abstract = "Consider k sets each consisting of n points in the plane, with each set allowed to move rigidly according to some continuous function of time. A paper by Aonuma, Imai, Imai, and Tokuyama shows an upper bound of O(n3k4log*n) on the number of combinatorial changes to the Voronoi diagram of the kn points over all time. We present a bound of O(n2k2λs(k)) for s fixed s, thus improving their result by slightly more than a factor of kn.",

keywords = "Analysis of algorithms, Voronoi diagrams, computational geometry",

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T1 - Voronoi diagrams of rigidly moving sets of points

AU - Huttenlocher, Daniel P.

AU - Kedem, Klara

AU - Kleinberg, Jon M.

PY - 1992/9/28

Y1 - 1992/9/28

N2 - Consider k sets each consisting of n points in the plane, with each set allowed to move rigidly according to some continuous function of time. A paper by Aonuma, Imai, Imai, and Tokuyama shows an upper bound of O(n3k4log*n) on the number of combinatorial changes to the Voronoi diagram of the kn points over all time. We present a bound of O(n2k2λs(k)) for s fixed s, thus improving their result by slightly more than a factor of kn.

AB - Consider k sets each consisting of n points in the plane, with each set allowed to move rigidly according to some continuous function of time. A paper by Aonuma, Imai, Imai, and Tokuyama shows an upper bound of O(n3k4log*n) on the number of combinatorial changes to the Voronoi diagram of the kn points over all time. We present a bound of O(n2k2λs(k)) for s fixed s, thus improving their result by slightly more than a factor of kn.

KW - Analysis of algorithms

KW - Voronoi diagrams

KW - computational geometry

UR - https://www.scopus.com/pages/publications/0040231871

U2 - 10.1016/0020-0190(92)90204-9

DO - 10.1016/0020-0190(92)90204-9

M3 - Article

AN - SCOPUS:0040231871

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SP - 217

EP - 223

JO - Information Processing Letters

JF - Information Processing Letters

IS - 4

ER -

Voronoi diagrams of rigidly moving sets of points

Abstract

Keywords

ASJC Scopus subject areas

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