Related papers: Expander Hierarchies for Normalized Cuts on Graphs

Expander graphs are highly connected sparse finite graphs. They play an important role in computer science as basic building blocks for network constructions, error correcting codes, algorithms and more. In recent years they have started to…

The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…

While advances in computing resources have made processing enormous amounts of data possible, human ability to identify patterns in such data has not scaled accordingly. Efficient computational methods for condensing and simplifying data…

Length-constrained expander decompositions are a new graph decomposition that has led to several recent breakthroughs in fast graph algorithms. Roughly, an $(h, s)$-length $\phi$-expander decomposition is a small collection of length…

Community detection in graphs has many important and fundamental applications including in distributed systems, compression, image segmentation, divide-and-conquer graph algorithms such as nested dissection, document and word clustering,…

Balanced partitioning is often a crucial first step in solving large-scale graph optimization problems, e.g., in some cases, a big graph can be chopped into pieces that fit on one machine to be processed independently before stitching the…

Graph clustering has many important applications in computing, but due to growing sizes of graphs, even traditionally fast clustering methods such as spectral partitioning can be computationally expensive for real-world graphs of interest.…

Graphs naturally appear in several real-world contexts including social networks, the web network, and telecommunication networks. While the analysis and the understanding of graph structures have been a central area of study in algorithm…

Spectral Clustering is one of the most traditional methods to solve segmentation problems. Based on Normalized Cuts, it aims at partitioning an image using an objective function defined by a graph. Despite their mathematical attractiveness,…

Graph-based clustering plays an important role in the clustering area. Recent studies about graph convolution neural networks have achieved impressive success on graph type data. However, in general clustering tasks, the graph structure of…

Graph classes of bounded tree rank were introduced recently in the context of the model checking problem for first-order logic of graphs. These graph classes are a common generalization of graph classes of bounded degree and bounded…

In this paper, we develop semi-external and external memory algorithms for graph partitioning and clustering problems. Graph partitioning and clustering are key tools for processing and analyzing large complex networks. We address both…

These are notes on the method of normalized graph cuts and its applications to graph clustering. I provide a fairly thorough treatment of this deeply original method due to Shi and Malik, including complete proofs. I include the necessary…

In this paper, we consider classic randomized low diameter decomposition procedures for planar graphs that obtain connected clusters which are cohesive in that close-by pairs of nodes are assigned to the same cluster with high probability.…

Hypergraphs, increasingly utilised to model complex and diverse relationships in modern networks, have gained significant attention for representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery…

Graph clustering is a fundamental technique in data analysis with applications in many different fields. While there is a large body of work on clustering undirected graphs, the problem of clustering directed graphs is much less understood.…

Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…

The continuous and rapid growth of highly interconnected datasets, which are both voluminous and complex, calls for the development of adequate processing and analytical techniques. One method for condensing and simplifying such datasets is…

Massive networks have shown that the determination of dense subgraphs, where vertices interact a lot, is necessary in order to visualize groups of common interest, and therefore be able to decompose a big graph into smaller structures. Many…

Graph clustering is an important algorithmic technique for analysing massive graphs, and has been widely applied in many research fields of data science. While the objective of most graph clustering algorithms is to find a vertex set of low…