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arXiv · 2211.04627

Computing (1+epsilon)-Approximate Degeneracy in Sublinear Time

Valerie King·Alex Thomo·Quinton Yong
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Abstract

The problem of finding the degeneracy of a graph is a subproblem of the k-core decomposition problem. In this paper, we present a (1 + epsilon)-approximate solution to the degeneracy problem which runs in O(n log n) time, sublinear in the input size for dense graphs, by sampling a small number of neighbors adjacent to high degree nodes. Our algorithm can also be extended to an O(n log n) time solution to the k-core decomposition problem. This improves upon the method by Bhattacharya et al., which implies a (4 + epsilon)-approximate ~O(n) solution to the degeneracy problem, and our techniques are similar to other sketching methods which use sublinear space for k-core and degeneracy. We prove theoretical guarantees of our algorithm and provide optimizations, which improve the running time of our algorithm in practice. Experiments on massive real-world web graphs show that our algorithm performs significantly faster than previous methods for computing degeneracy, including the 2022 exact degeneracy algorithm by Li et al.

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Valerie King, Alex Thomo, Quinton Yong. 2022-11-09. Computing (1+epsilon)-Approximate Degeneracy in Sublinear Time. https://arxiv.org/abs/2211.04627

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