Computing (1+epsilon)-Approximate Degeneracy in Sublinear Time
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.
Cite
@article{arxiv.2211.04627,
title = {Computing (1+epsilon)-Approximate Degeneracy in Sublinear Time},
author = {Valerie King and Alex Thomo and Quinton Yong},
journal= {arXiv preprint arXiv:2211.04627},
year = {2022}
}