Connected k-Center and k-Diameter Clustering Article Swipe
Lukas Drexler
,
Jan Eube
,
Kelin Luo
,
Dorian Reineccius
,
Heiko Röglin
,
Melanie Schmidt
,
Julian Wargalla
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1007/s00453-024-01266-9
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.1007/s00453-024-01266-9
Motivated by an application from geodesy, we study the connected k-center problem and the connected k-diameter problem . The former problem has been introduced by Ge et al. (ACM Trans Knowl Discov Data 2(2):1–35, 2008. https://doi.org/10.1145/1376815.1376816 ) to model clustering of data sets with both attribute and relationship data. These problems arise from the classical k -center and k -diameter problems by adding a side constraint. For the side constraint, we are given an undirected connectivity graph G on the input points, and a clustering is now only feasible if every cluster induces a connected subgraph in G . Usually in clustering problems one assumes that the clusters are pairwise disjoint. We study this case but additionally also the case that clusters are allowed to be non-disjoint. This can help to satisfy the connectivity constraints. Our main result is an $$O(\log ^2k)$$ -approximation algorithm for the disjoint connected k -center and k -diameter problem. For Euclidean spaces of constant dimension and for metrics with constant doubling dimension, the approximation factor improves to O (1). Our algorithm works by computing a non-disjoint connected clustering first and transforming it into a disjoint connected clustering. We complement these upper bounds by several upper and lower bounds for variations and special cases of the model.
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- article
- Language
- en
- Landing Page
- https://doi.org/10.1007/s00453-024-01266-9
- OA Status
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https://doi.org/10.1007/s00453-024-01266-9Digital Object Identifier
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Connected k-Center and k-Diameter ClusteringWork title
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articleOpenAlex work type
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enPrimary language
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2024Year of publication
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2024-09-02Full publication date if available
- Authors
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Lukas Drexler, Jan Eube, Kelin Luo, Dorian Reineccius, Heiko Röglin, Melanie Schmidt, Julian WargallaList of authors in order
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https://doi.org/10.1007/s00453-024-01266-9Publisher landing page
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hybridOpen access status per OpenAlex
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https://doi.org/10.1007/s00453-024-01266-9Direct OA link when available
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Center (category theory), Combinatorics, Cluster analysis, Computer science, k-means clustering, Theory of computation, Mathematics, Algorithm, Artificial intelligence, Crystallography, ChemistryTop concepts (fields/topics) attached by OpenAlex
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| referenced_works | https://openalex.org/W1965792576, https://openalex.org/W1983197449, https://openalex.org/W1994946127, https://openalex.org/W1973264045, https://openalex.org/W2044028871, https://openalex.org/W1604056673, https://openalex.org/W1978270739, https://openalex.org/W2947657760, https://openalex.org/W1836068669, https://openalex.org/W3203345503, https://openalex.org/W1680732213, https://openalex.org/W3083108821, https://openalex.org/W2154044080, https://openalex.org/W2114589083, https://openalex.org/W2593080689, https://openalex.org/W2005694048, https://openalex.org/W2055996587, https://openalex.org/W2964242853, https://openalex.org/W2959606821, https://openalex.org/W2964077180, https://openalex.org/W2767218854, https://openalex.org/W2596841574, https://openalex.org/W2522382150, https://openalex.org/W2167389897, https://openalex.org/W2160296932, https://openalex.org/W1998544343, https://openalex.org/W2401610261, https://openalex.org/W2019062750 |
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