TY - JOUR

T1 - Efficient enumeration of maximal induced bicliques

AU - Hermelin, Danny

AU - Manoussakis, George

N1 - Funding Information:
This research was supported by Grant No. 2016049 from the United States–Israel Binational Science Foundation (BSF) .
Publisher Copyright:
© 2021

PY - 2021/11/15

Y1 - 2021/11/15

N2 - 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.

AB - 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.

KW - algorithms

KW - enumeration

KW - graphs

UR - http://www.scopus.com/inward/record.url?scp=85086568921&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2020.04.034

DO - 10.1016/j.dam.2020.04.034

M3 - Article

AN - SCOPUS:85086568921

VL - 303

SP - 253

EP - 261

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -