Agglomerative clustering of growing squares

Thom Castermans; Bettina Speckmann; Frank Staals; Kevin Verbeek

doi:10.1007/978-3-319-77404-6_20

Agglomerative clustering of growing squares

Thom Castermans, Bettina Speckmann, Frank Staals, Kevin Verbeek

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

4 Citations (Scopus)

234 Downloads (Pure)

Abstract

We study an agglomerative clustering problem motivated by interactive glyphs in geo-visualization. Consider a set of disjoint square glyphs on an interactive map. When the user zooms out, the glyphs grow in size relative to the map, possibly with different speeds. When two glyphs intersect, we wish to replace them by a new glyph that captures the information of the intersecting glyphs. We present a fully dynamic kinetic data structure that maintains a set of n disjoint growing squares. Our data structure uses O(n(log n log log n)²) space, supports queries in worst case O(log³ n) time, and updates in O(log⁷n) amortized time. This leads to an O(n α(n) log⁷n) time algorithm (where α is the inverse Ackermann function) to solve the agglomerative clustering problem, which is a significant improvement over the straightforward O(n² log n) time algorithm.

Original language	English
Title of host publication	13th Latin American Theoretical INformatics Symposium (LATIN)
Editors	M.A. Bender, M. Farach-Colton, M.A. Mosteiro
Place of Publication	Berlin
Publisher	Springer
Pages	260-274
Number of pages	15
ISBN (Print)	9783319774039
DOIs	https://doi.org/10.1007/978-3-319-77404-6_20
Publication status	Published - 1 Jan 2018
Event	13th Latin American Theoretical INformatics Symposium (LATIN 2018) - Buenos Aires, Argentina Duration: 16 Apr 2018 → 19 Apr 2018 Conference number: 13 http://latin2018.dc.uba.ar/

Publication series

Name	Lecture Notes in Computer Science
Volume	10807
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Name	Theoretical Computer Science and General Issues
Volume	10807

Conference

Conference	13th Latin American Theoretical INformatics Symposium (LATIN 2018)
Abbreviated title	LATIN 2018
Country/Territory	Argentina
City	Buenos Aires
Period	16/04/18 → 19/04/18
Internet address	http://latin2018.dc.uba.ar/

Funding

The Netherlands Organisation for Scientific Research (NWO) is supporting T. Castermans (project number 314.99.117), B. Speckmann (project number 639.023.208), F. Staals (project number 612.001.651), and K. Verbeek (project num-ber 639.021.541). 1 http://glammap.net/glamdev/maps/1, best viewed in Chrome. GlamMap currently does not implement the algorithm described in this article.

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10.1007/978-3-319-77404-6_20

agglomerative-clustering-growingFinal author version , 668 KBLicence: Unspecified

Cite this

Castermans, T., Speckmann, B., Staals, F., & Verbeek, K. (2018). Agglomerative clustering of growing squares. In M. A. Bender, M. Farach-Colton, & M. A. Mosteiro (Eds.), 13th Latin American Theoretical INformatics Symposium (LATIN) (pp. 260-274). (Lecture Notes in Computer Science; Vol. 10807), (Theoretical Computer Science and General Issues; Vol. 10807). Springer. https://doi.org/10.1007/978-3-319-77404-6_20

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title = "Agglomerative clustering of growing squares",

abstract = "We study an agglomerative clustering problem motivated by interactive glyphs in geo-visualization. Consider a set of disjoint square glyphs on an interactive map. When the user zooms out, the glyphs grow in size relative to the map, possibly with different speeds. When two glyphs intersect, we wish to replace them by a new glyph that captures the information of the intersecting glyphs. We present a fully dynamic kinetic data structure that maintains a set of n disjoint growing squares. Our data structure uses O(n(log n log log n)2) space, supports queries in worst case O(log3 n) time, and updates in O(log7 n) amortized time. This leads to an O(n α(n) log7 n) time algorithm (where α is the inverse Ackermann function) to solve the agglomerative clustering problem, which is a significant improvement over the straightforward O(n2 log n) time algorithm.",

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Castermans, T, Speckmann, B, Staals, F & Verbeek, K 2018, Agglomerative clustering of growing squares. in MA Bender, M Farach-Colton & MA Mosteiro (eds), 13th Latin American Theoretical INformatics Symposium (LATIN). Lecture Notes in Computer Science, vol. 10807, Theoretical Computer Science and General Issues, vol. 10807, Springer, Berlin, pp. 260-274, 13th Latin American Theoretical INformatics Symposium (LATIN 2018), Buenos Aires, Argentina, 16/04/18. https://doi.org/10.1007/978-3-319-77404-6_20

Agglomerative clustering of growing squares. / Castermans, Thom; Speckmann, Bettina; Staals, Frank et al.
13th Latin American Theoretical INformatics Symposium (LATIN). ed. / M.A. Bender; M. Farach-Colton; M.A. Mosteiro. Berlin: Springer, 2018. p. 260-274 (Lecture Notes in Computer Science; Vol. 10807), (Theoretical Computer Science and General Issues; Vol. 10807).

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

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N2 - We study an agglomerative clustering problem motivated by interactive glyphs in geo-visualization. Consider a set of disjoint square glyphs on an interactive map. When the user zooms out, the glyphs grow in size relative to the map, possibly with different speeds. When two glyphs intersect, we wish to replace them by a new glyph that captures the information of the intersecting glyphs. We present a fully dynamic kinetic data structure that maintains a set of n disjoint growing squares. Our data structure uses O(n(log n log log n)2) space, supports queries in worst case O(log3 n) time, and updates in O(log7 n) amortized time. This leads to an O(n α(n) log7 n) time algorithm (where α is the inverse Ackermann function) to solve the agglomerative clustering problem, which is a significant improvement over the straightforward O(n2 log n) time algorithm.

AB - We study an agglomerative clustering problem motivated by interactive glyphs in geo-visualization. Consider a set of disjoint square glyphs on an interactive map. When the user zooms out, the glyphs grow in size relative to the map, possibly with different speeds. When two glyphs intersect, we wish to replace them by a new glyph that captures the information of the intersecting glyphs. We present a fully dynamic kinetic data structure that maintains a set of n disjoint growing squares. Our data structure uses O(n(log n log log n)2) space, supports queries in worst case O(log3 n) time, and updates in O(log7 n) amortized time. This leads to an O(n α(n) log7 n) time algorithm (where α is the inverse Ackermann function) to solve the agglomerative clustering problem, which is a significant improvement over the straightforward O(n2 log n) time algorithm.

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ER -

Agglomerative clustering of growing squares

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