We consider the problem of finding planted bicliques in random matrices over GF [q]. That is, our input matrix is a GF [q]-sum of an unknown biclique (rank-1 matrix) and a random matrix. We study different models for the random graphs and characterize the conditions when the planted biclique can be recovered. We also empirically show that a simple heuristic can reliably recover the planted bicl...

In this paper, we introduce the maximum edge biclique problem in bipartite graphs and the edge/node weighted multipartite clique problem in multipartite graphs. Our motivation for studying these problems came from abstractions of real manufacturing problems in the computer industry and from formal concept analysis. We show that the weighted version and four variants of the unweighted version of...

The biclique graph of G, KB(G), is the intersection graph of the bicliques of G. Given a graph G, the iterated biclique graph of G, KBk(G), is the graph defined iteratively as follows: KBk+1(G) = KB(KBk(G)). Say that a graph G diverges (resp. converges) under the operator KB whenever limk→∞ |V (KBk(G))| = ∞ (resp. limk→∞KB(G) = KBm(G) for some m). Each of these behaviours were recently characte...

Abstract. SQUARE is an iterated block cipher proposed by Daemen et.al. in FSE1997. Inspired by Bogdanov et.al.’s recent works [12], we first present an improved biclique attack, i.e. stat-based independent biclique attack on full rounds SQUARE in this paper. We construct a one round stat-based independent biclique for the initial round, and utilize matching with precomputation techniques to rec...

Given a complete bipartite graph G = (V1, V2, E) where edges take on both positive and negative weights from set S, the maximum weighted edge biclique problem, or S-MWEB for short, asks to find a biclique subgraph whose sum of edge weights is maximized. This problem has various applications in bioinformatics, machine learning and databases and its (in)approximability remains open. In this paper...

The problem of finding large complete subgraphs in bipartite graphs (that is, bicliques) is a well-known combinatorial optimization problem referred to as the maximum-edge biclique problem (MBP), and has many applications, e.g., in web community discovery, biological data analysis and text mining. In this paper, we present a new continuous characterization for MBP. Given a bipartite graphG, we ...

Due to a large number of applications, bicliques of graphs have been widely considered in the literature. This paper focuses on non-induced bicliques. Given a graph G = (V,E) on n vertices, a pair (X,Y ), with X,Y ⊆ V , X ∩ Y = ∅, is a non-induced biclique if {x, y} ∈ E for any x ∈ X and y ∈ Y . The NP-complete problem of finding a non-induced (k1, k2)-biclique asks to decide whether G contains...

In graph theory, the Helly property has been applied to families of sets, such as cliques, disks, bicliques, and neighbourhoods, leading to the classes of clique-Helly, disk-Helly, biclique-Helly, neighbourhood-Helly graphs, respectively. A natural question is to determine for which graphs the corresponding Helly property holds, for every induced subgraph. This leads to the corresponding classe...

A biclique is a maximal induced complete bipartite subgraph of a graph. We investigate the intersection structure of edge-sets of bicliques in a graph. Specifically, we study the associated edge-biclique hypergraph whose hyperedges are precisely the edge-sets of all bicliques. We characterize graphs whose edgebiclique hypergraph is conformal (i.e., it is the clique hypergraph of its 2-section) ...