Related papers: Further Algebraic Algorithms in the Congested Cliq…
While algebrisation constitutes a powerful technique in the design and analysis of centralised algorithms, to date there have been hardly any applications of algebraic techniques in the context of distributed graph algorithms. This work is…
In this work, we use algebraic methods for studying distance computation and subgraph detection tasks in the congested clique model. Specifically, we adapt parallel matrix multiplication implementations to the congested clique, obtaining an…
The congested clique model of distributed computing has been receiving attention as a model for densely connected distributed systems. While there has been significant progress on the side of upper bounds, we have very little in terms of…
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…
Graph problems are troublesome when it comes to MapReduce. Typically, to be able to design algorithms that make use of the advantages of MapReduce, assumptions beyond what the model imposes, such as the density of the input graph, are…
We provide a fast distributed algorithm for detecting $h$-cycles in the \textsf{Congested Clique} model, whose running time decreases as the number of $h$-cycles in the graph increases. In undirected graphs, constant-round algorithms are…
This study addresses a distributed optimization with a novel class of coupling of variables, called clique-wise coupling. A clique is a node set of a complete subgraph of an undirected graph. This setup is an extension of pairwise coupled…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
In this paper we give fast distributed graph algorithms for detecting and listing small subgraphs, and for computing or approximating the girth. Our algorithms improve upon the state of the art by polynomial factors, and for girth, we…
Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…
This paper gives simple distributed algorithms for the fundamental problem of computing graph distances in the Congested Clique model. One of the main components of our algorithms is fast matrix multiplication, for which we show an…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
The {Congested Clique} is a distributed-computing model for single-hop networks with restricted bandwidth that has been very intensively studied recently. It models a network by an $n$-vertex graph in which any pair of vertices can…
As it follows from G\"odel's incompleteness theorems, any consistent formal system of axioms and rules of inference should imply a true unprovable statement. Actually, this fundamental principle can be efficiently applicable in…
There are well established reductions between combinatorial sampling and counting problems (Jerrum, Valiant, Vazirani TCS 1986). Building off of a very recent parallel algorithm utilizing this connection (Liu, Yin, Zhang arxiv 2024), we…
Biclustering, also known as co-clustering or two-way clustering, simultaneously partitions the rows and columns of a data matrix to reveal submatrices with coherent patterns. Incorporating background knowledge into clustering to enhance…
The congested clique model is a message-passing model of distributed computation where the underlying communication network is the complete graph of $n$ nodes. In this paper we consider the situation where the joint input to the nodes is an…
We provide a novel family of generative block-models for random graphs that naturally incorporates degree distributions: the block-constrained configuration model. Block-constrained configuration models build on the generalised…
Community-based graph clustering is one of the most popular topics in the analysis of complex social networks. This type of clustering involves grouping vertices that are considered to share more connections, whereas vertices in different…
Chordal decomposition techniques are used to reduce large structured positive semidefinite matrix constraints in semidefinite programs (SDPs). The resulting equivalent problem contains multiple smaller constraints on the nonzero blocks (or…