Fully-Scalable MPC Algorithms for Clustering in High Dimension
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10493446" target="_blank" >RIV/00216208:11320/24:10493446 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4230/LIPIcs.ICALP.2024.50" target="_blank" >https://doi.org/10.4230/LIPIcs.ICALP.2024.50</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.ICALP.2024.50" target="_blank" >10.4230/LIPIcs.ICALP.2024.50</a>
Alternative languages
Result language
angličtina
Original language name
Fully-Scalable MPC Algorithms for Clustering in High Dimension
Original language description
We design new parallel algorithms for clustering in high-dimensional Euclidean spaces. These algorithms run in the Massively Parallel Computation (MPC) model, and are fully scalable, meaning that the local memory in each machine may be n^σ for arbitrarily small fixed σ > 0. Importantly, the local memory may be substantially smaller than the number of clusters k, yet all our algorithms are fast, i.e., run in O(1) rounds.We first devise a fast MPC algorithm for O(1)-approximation of uniform Facility Location. This is the first fully-scalable MPC algorithm that achieves O(1)-approximation for any clustering problem in general geometric setting; previous algorithms only provide poly(log n)-approximation or apply to restricted inputs, like low dimension or small number of clusters k; e.g. [Bhaskara and Wijewardena, ICML'18; Cohen-Addad et al., NeurIPS'21; Cohen-Addad et al., ICML'22]. We then build on this Facility Location result and devise a fast MPC algorithm that achieves O(1)-bicriteria approximation for k-Median and for k-Means, namely, it computes (1+ε)k clusters of cost within O(1/ε2)-factor of the optimum for k clusters.A primary technical tool that we introduce, and may be of independent interest, is a new MPC primitive for geometric aggregation, namely, computing for every data point a statistic of its approximate neighborhood, for statistics like range counting and nearest-neighbor search. Our implementation of this primitive works in high dimension, and is based on consistent hashing (aka sparse partition), a technique that was recently used for streaming algorithms [Czumaj et al., FOCS'22].
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/GA22-22997S" target="_blank" >GA22-22997S: Efficient and Realistic Models in Computational Social Choice</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Leibniz International Proceedings in Informatics, LIPIcs
ISBN
978-3-95977-322-5
ISSN
1868-8969
e-ISSN
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Number of pages
20
Pages from-to
1-20
Publisher name
Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Place of publication
Dagstuhl, Germany
Event location
Tallin, Estonsko
Event date
Jul 8, 2024
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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