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Sublinear Time and Space Algorithms for Correlation Clustering via Sparse-Dense Decompositions

Authors Sepehr Assadi, Chen Wang

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Sepehr Assadi
  • Department of Computer Science, Rutgers University, Piscataway, NJ, USA
Chen Wang
  • Department of Computer Science, Rutgers University, Piscataway, NJ, USA

Funding

This work is supported in part by a NSF CAREER Grant CCF-2047061, and a gift from Google Research.

Acknowledgements

We thank the anonymous reviewers of ITCS 2022 for their many insightful suggestions that helped with improving the presentation of this paper.

Cite AsGet BibTex

Sepehr Assadi and Chen Wang. Sublinear Time and Space Algorithms for Correlation Clustering via Sparse-Dense Decompositions. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 10:1-10:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.ITCS.2022.10

Abstract

We present a new approach for solving (minimum disagreement) correlation clustering that results in sublinear algorithms with highly efficient time and space complexity for this problem. In particular, we obtain the following algorithms for n-vertex (+/-)-labeled graphs G: - A sublinear-time algorithm that with high probability returns a constant approximation clustering of G in O(nlog²n) time assuming access to the adjacency list of the (+)-labeled edges of G (this is almost quadratically faster than even reading the input once). Previously, no sublinear-time algorithm was known for this problem with any multiplicative approximation guarantee. - A semi-streaming algorithm that with high probability returns a constant approximation clustering of G in O(n log n) space and a single pass over the edges of the graph G (this memory is almost quadratically smaller than input size). Previously, no single-pass algorithm with o(n²) space was known for this problem with any approximation guarantee. The main ingredient of our approach is a novel connection to sparse-dense graph decompositions that are used extensively in the graph coloring literature. To our knowledge, this connection is the first application of these decompositions beyond graph coloring, and in particular for the correlation clustering problem, and can be of independent interest.

Subject Classification

ACM Subject Classification
  • Theory of computation → Streaming, sublinear and near linear time algorithms
  • Computing methodologies → Machine learning
Keywords
  • Correlation Clustering
  • Sublinear Algorithms
  • Semi-streaming Algorithms
  • Sublinear time Algorithms

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