Memory-Efficient Approximation Algorithms for Max-k-Cut and Correlation Clustering

Nimita Shinde; Vishnu Narayanan; James Saunderson

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arXiv · 2110.00779

Memory-Efficient Approximation Algorithms for Max-k-Cut and Correlation Clustering

Nimita Shinde·Vishnu Narayanan·James Saunderson

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Abstract

Max-k-Cut and correlation clustering are fundamental graph partitioning problems. For a graph with G=(V,E) with n vertices, the methods with the best approximation guarantees for Max-k-Cut and the Max-Agree variant of correlation clustering involve solving SDPs with $O(n^2)$ variables and constraints. Large-scale instances of SDPs, thus, present a memory bottleneck. In this paper, we develop simple polynomial-time Gaussian sampling-based algorithms for these two problems that use $O(n+|E|)$ memory and nearly achieve the best existing approximation guarantees. For dense graphs arriving in a stream, we eliminate the dependence on $|E|$ in the storage complexity at the cost of a slightly worse approximation ratio by combining our approach with sparsification.

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BibTeX RIS

Nimita Shinde, Vishnu Narayanan, James Saunderson. 2021-10-02. Memory-Efficient Approximation Algorithms for Max-k-Cut and Correlation Clustering. https://arxiv.org/abs/2110.00779

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