Parameterized Approximation Algorithms for K-center Clustering and Variants

Authors: Sayan Bandyapadhyay, Zachary Friggstad, Ramin Mousavi3895-3903

AAAI 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical We give a faster algorithm for small dimensions: roughly speaking an O (2O((1/ϵ)O(d) k1 1/d log k))-time (1 + ϵ)-approximation. In particular, the running time is roughly O (2O((1/ϵ)O(1) k log k)) in the plane. We complement our algorithmic result with a matching hardness lower bound. We also consider a well-studied generalization of k-center, called Non-uniform k-center (NUk C), where we allow different radii clusters. NUk C is NP-hard to approximate within any factor, even in the Euclidean case. We design a 2O(k log k)n2 time 3-approximation for NUk C in general metrics, and a 2O((k log k)/ϵ)dn time (1 + ϵ)-approximation for Euclidean NUk C.
Researcher Affiliation Academia Sayan Bandyapadhyay1, Zachary Friggstad2, Ramin Mousavi2 1 Department of Informatics, University of Bergen, Norway 2 Department of Computing Science, University of Alberta, Canada
Pseudocode No The paper describes algorithmic steps in prose (e.g., 'Preliminary Step: Reducing to a feasibility check', 'Step 1: Reducing the input size', 'The Algorithm.') but does not present them as structured pseudocode blocks or clearly labeled algorithm environments.
Open Source Code No The paper does not provide any links or statements about the availability of open-source code for the described methodology.
Open Datasets No The paper is theoretical and does not conduct experiments with datasets, so no dataset access information is provided.
Dataset Splits No The paper is theoretical and does not conduct experiments with datasets, so no training/validation/test dataset splits are provided.
Hardware Specification No The paper is theoretical and does not report on experiments requiring hardware, so no hardware specifications are mentioned.
Software Dependencies No The paper is theoretical and does not report on experiments, so it does not list specific software dependencies with version numbers.
Experiment Setup No The paper is theoretical and does not describe any experimental setup details such as hyperparameters or training configurations.