Parameterized complexity of categorical clustering with size constraints

In the Categorical Clustering problem, we are given a set of vectors (matrix) A={a1,…,an} over Σm, where Σ is a finite alphabet, and integers k and B. The task is to partition A into k clusters such that the median objective of the clustering in the Hamming norm is at most B. Fomin, Golovach, and Pa...

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Vydané v:	Journal of computer and system sciences Ročník 136; s. 171 - 194
Hlavní autori:	Fomin, Fedor V., Golovach, Petr A., Purohit, Nidhi
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier Inc 01.09.2023
Predmet:	Categorical clustering Fixed-parameterized algorithm k-median Kernelization k-median Fixed-parameterized algorithm Categorical clustering Kernelization
ISSN:	0022-0000, 1090-2724
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Popis
Shrnutí:	In the Categorical Clustering problem, we are given a set of vectors (matrix) A={a1,…,an} over Σm, where Σ is a finite alphabet, and integers k and B. The task is to partition A into k clusters such that the median objective of the clustering in the Hamming norm is at most B. Fomin, Golovach, and Panolan [ICALP 2018] proved that the problem is fixed-parameter tractable for the binary case Σ={0,1}. We extend this algorithmic result to a popular capacitated clustering model, where in addition the sizes of the clusters are lower and upper bounded by integer parameters p and q, respectively. Our main theorem is that the problem is solvable in time 2O(Blog⁡B)\|Σ\|B⋅(mn)O(1).
ISSN:	0022-0000 1090-2724
DOI:	10.1016/j.jcss.2023.03.006