k-clique listing is a vital graph mining operator with diverse applications
in various networks. The state-of-the-art algorithms all adopt a
branch-and-bound (BB) framework with a vertex-oriented branching strategy
(called VBBkC), which forms a sub-branch by expanding a partial k-clique with
a vertex. These algorithms have the time complexity of O(km(δ/2)k−2), where m is the number of edges in the graph and δ
is the degeneracy of the graph. In this paper, we propose a BB framework with a
new edge-oriented branching (called EBBkC), which forms a sub-branch by
expanding a partial k-clique with two vertices that connect each other (which
correspond to an edge). We explore various edge orderings for EBBkC such that
it achieves a time complexity of O(δm+km(τ/2)k−2), where
Ï„ is an integer related to the maximum truss number of the graph and we
have τ<δ. The time complexity of EBBkC is better than that of VBBkC
algorithms for k>3 since both O(δm) and O(km(τ/2)k−2) are
bounded by O(km(δ/2)k−2). Furthermore, we develop specialized
algorithms for sub-branches on dense graphs so that we can early-terminate them
and apply the specialized algorithms. We conduct extensive experiments on 19
real graphs, and the results show that our newly developed EBBkC-based
algorithms with the early termination technique consistently and largely
outperform the state-of-the-art (VBBkC-based) algorithms.Comment: This paper has been accepted by SIGMOD 202