Fast Maximal Cliques Enumeration in Sparse Graphs |
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Authors: | Lijun Chang Jeffrey Xu Yu Lu Qin |
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Affiliation: | 1. The Chinese University of Hong Kong, Hong Kong, China
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Abstract: | In this paper, we consider the problem of generating all maximal cliques in a sparse graph in polynomial delay. Given a graph G=(V,E) with n vertices and m edges, the latest and fastest polynomial delay algorithm for sparse graphs enumerates all maximal cliques in O(Δ 4) time delay, where Δ is the maximum degree of vertices. However, it requires an O(n?m) preprocessing time. We improve it in two aspects. First, our algorithm does not need preprocessing. Therefore, our algorithm is a truly polynomial delay algorithm. Second, our algorithm enumerates all maximal cliques in O(Δ?H 3) time delay, where H is the so called H-value of a graph or equivalently it is the smallest integer satisfying |{v∈V∣δ(v)≥H}|≤H given δ(v) as the degree of a vertex. In real-world network data, H usually is a small value and much smaller than Δ. |
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