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

TL;DR

This paper introduces a fast, sublinear-time algorithm for approximating graph degeneracy within a (1+epsilon) factor, significantly improving efficiency over previous methods, especially on large dense graphs.

Contribution

The paper presents a novel (1+epsilon)-approximate algorithm for degeneracy that runs in O(n log n) time, extending to k-core decomposition, with proven guarantees and practical optimizations.

Findings

Runs in O(n log n) time, sublinear for dense graphs

Outperforms previous approximate and exact algorithms in speed

Effective on large real-world web graphs

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.