TY - JOUR
AU - Qin, Lu
AB - 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.
TI - Fast Maximal Cliques Enumeration in Sparse Graphs
JF - Algorithmica
DO - 10.1007/s00453-012-9632-8
DA - 2012-03-06
UR - https://www.deepdyve.com/lp/springer-journals/fast-maximal-cliques-enumeration-in-sparse-graphs-I5lihuDbvk
SP - 173
EP - 186
VL - 66
IS - 1
DP - DeepDyve
ER -