Related papers: Towards a complexity theory for the congested cliq…
Bonne and Censor-Hillel (ICALP 2019) initiated the study of distributed subgraph finding in dynamic networks of limited bandwidth. For the case where the target subgraph is a clique, they determined the tight bandwidth complexity bounds in…
In this paper, we study distributed graph algorithms in networks in which the nodes have a limited communication capacity. Many distributed systems are built on top of an underlying networking infrastructure, for example by using a virtual…
$k$-defective cliques relax cliques by allowing up-to $k$ missing edges from being a complete graph. This relaxation enables us to find larger near-cliques and has applications in link prediction, cluster detection, social network analysis…
We consider locally checkable labeling LCL problems in the LOCAL model of distributed computing. Since 2016, there has been a substantial body of work examining the possible complexities of LCL problems. For example, it has been established…
The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on…
It was experimentally observed that the majority of real-world networks follow power law degree distribution. The aim of this paper is to study the algorithmic complexity of such "typical" networks. The contribution of this work is twofold.…
We propose and study a hierarchical algorithm to generate graphs having a predetermined distribution of cliques, the fully connected subgraphs. The construction mechanism may be either random or incorporate preferential attachment. We…
The planted clique problem is well-studied in the context of observing, explaining, and predicting interesting computational phenomena associated with statistical problems. When equating computational efficiency with the existence of…
In a distinguishing problem, the input is a sample drawn from one of two distributions and the algorithm is tasked with identifying the source distribution. The performance of a distinguishing algorithm is measured by its advantage, i.e.,…
We begin development of a method for studying dynamical systems using concepts from computational complexity theory. We associate families of decision problems, called telic problems, to dynamical systems of a certain class. These decision…
Contagion processes have been proven to fundamentally depend on the structural properties of the interaction networks conveying them. Many real networked systems are characterized by clustered substructures representing either collections…
We consider the problem of identifying a maximum clique in a given graph. We have proposed a mathematical model for this problem. The model resembles the matrix decomposition of the adjacency matrix of a given graph. The objective function…
Subgraph detection has recently been one of the most studied problems in the CONGEST model of distributed computing. In this work, we study the distributed complexity of problems closely related to subgraph detection, mainly focusing on…
Many real networks have cliques as their constitutional units. Here we present a family of scale-free network model consist of cliques, which is established by a simple recursive algorithm. We investigate the networks both analytically and…
The problem of categorical data analysis in high dimensions is considered. A discussion of the fundamental difficulties of probability modeling is provided, and a solution to the derivation of high dimensional probability distributions…
It has been shown that many networks associated with complex systems are small-world (they have both a large local clustering coefficient and a small diameter) and they are also scale-free (the degrees are distributed according to a power…
The recent advent of programmable switches makes distributed algorithms readily deployable in real-world datacenter networks. However, there are still gaps between theory and practice that prevent the smooth adaptation of CONGEST algorithms…
We introduce Clique Matrices as an alternative representation of undirected graphs, being a generalisation of the incidence matrix representation. Here we use clique matrices to decompose a graph into a set of possibly overlapping clusters,…
Hierarchical clustering is a popular unsupervised data analysis method. For many real-world applications, we would like to exploit prior information about the data that imposes constraints on the clustering hierarchy, and is not captured by…
In this paper, we study the graph realization problem in the Congested Clique model of distributed computing under crash faults. We consider {\em degree-sequence realization}, in which each node $v$ is associated with a degree value $d(v)$,…