Computing (1+ϵ)-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 + ϵ)-approximate solution to the degeneracy problem which runs in O(n log n) time on a graph with n nodes, sublinear in the input size for dense graphs, by sampling a small number of neighbours 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 + ϵ)-approximate ˜O(n) solution to the degeneracy problem. 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.