问题
Given is a bipartite graph, and we want to list all maximal complete bipartite sub-graph.
For instance,
vertex set L = {A, B, C, D}
vertex set R = {a, b, c, d, e}
edges: A-a, A-b, B-a, B-b, C-c, C-d, D-c, D-d, D-e
The maximal complete bipartite are:
{A,B}-{a, b}
{C,D}-{c, d}
{D} - {c, d, e}
I have found a brute force algorithm, O(2^n). I don't know if some approximation algorithm or randomized algorithm.
回答1:
You can transform the problem to finding maximal cliques by adding edges between every pair of vertices in each part of the bipartite graph.
The Bron-Kerbosch algorithm can be used to list all maximal cliques in a graph (not necessarily bipartite). It is pretty easy to implement and has a slightly better worst-case time bound of O(3^(n/3)). There is also a fix-parameter tractable time bound in term of the degeneracy of the graph.
来源：https://stackoverflow.com/questions/15699714/find-all-maximal-complete-bipartite-subgraph-from-given-bipartite-graph