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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Bibliographic Details
Published in:Journal of computer and system sciences Vol. 136; pp. 171 - 194
Main Authors: Fomin, Fedor V., Golovach, Petr A., Purohit, Nidhi
Format: Journal Article
Language:English
Published: Elsevier Inc 01.09.2023
Subjects:
Categorical clustering
Fixed-parameterized algorithm
k-median
Kernelization
k-median
Fixed-parameterized algorithm
Categorical clustering
Kernelization
ISSN:0022-0000, 1090-2724
Online Access:Get full text
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Summary: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