Computing (1+ϵ)-Approximate Degeneracy in Sublinear Time
Date
2022-12-21
Authors
Yong, Quinton
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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 + 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.
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Keywords
Graphs, k-core, Degeneracy, Sublinear, Approximate, Randomized Algorithm