Given a graph G of order n, we consider the problem of enumerating all its maximal induced bicliques. We first propose an algorithm running in time O(n3n/3). As the maximum number of maximal induced bicliques of a graph with n vertices is Θ(3n/3), the algorithm is worst-case output size optimal. Then, we prove new bounds on the maximum number of maximal induced bicliques of graphs with respect to their maximum degree Δ and degeneracy k, and propose a near-optimal algorithm with enumeration time O(nk(Δ+k)3[Formula presented]). Then, we provide output sensitive algorithms for this problem with enumeration time depending only on the maximum degree of the input graph. Since we need to store the bicliques in these algorithms, the space complexity may be exponential. Thus, we show how to modify them so they only require polynomial space, but with a slight time complexity increase.
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics