In this work, we apply the sliced biclique cryptanalysis technique to show 8-round collision attack on a hash function H based on 4-branch, Type-2 Generalized Feistel Network (Type-2 GFN). This attack is generic and works on 4-branch, Type-2 GFN with any parameters including the block size, type of round function, the number of S-boxes in each round and the number of SP layers inside the round ...

The Small Set Expansion Hypothesis is a conjecture which roughly states that it is NP-hard to distinguish between a graph with a small subset of vertices whose (edge) expansion is almost zero and one in which all small subsets of vertices have expansion almost one. In this work, we prove conditional inapproximability results with essentially optimal ratios for the following graph problems based...

The biclique problem asks, given a graph G and a parameter k, whether G has a complete bipartite subgraph of k vertices in each part (a biclique of order k). Fixed-parameter tractability of this problem is a longstanding open question in parameterized complexity that received a lot of attention from the community. In this paper we consider a restricted version of this problem by introducing an ...

Given a graph G and a parameter k, the k-biclique problem asks whether G contains a complete bipartite subgraph Kk,k. This is the most easily stated problem on graphs whose parameterized complexity is still unknown. We provide an fpt-reduction from k-clique to k-biclique, thus solving this longstanding open problem. Our reduction use a class of bipartite graphs with a threshold property of inde...

In this paper, we consider the minimum biclique cover and minimum biclique partition problems on bipartite graphs. In the minimum biclique cover problem, we are given an input bipartite graph G = (V,E), and our goal is to compute the minimum number of complete bipartite subgraphs that cover all edges of G. This problem, besides its correspondence to a well-studied notion of bipartite dimension ...

We present here 2-approximation algorithms for several node deletion and edge deletion biclique problems and for an edge deletion clique problem. The biclique problem is to find a node induced subgraph that is bipartite and complete. The objective is to minimize the total weight of nodes or edges deleted so that the remaining subgraph is bipartite complete. Several variants of the biclique prob...

Pseudo-bicliques model various problems encountered in bio-informatics, data mining and networks. They relax the rigid connectivity requirement of bicliques to cater missing and noisy data. In this paper, we consider the weighted density based model of pseudo-biclique. This model defines pseudo-biclique as a bipartite subgraph such that the ratio of the number of its edges to the number of edge...

We consider computational problems on covering graphs with bicliques (complete bipartite subgraphs). Given a graph and an integer k, the biclique cover problem asks whether the edge-set of the graph can be covered with at most k bicliques; the biclique partition problem is defined similarly with the additional condition that the bicliques are required to be mutually edge-disjoint. The biclique ...