Related papers: Efficient Core Maintenance in Large Dynamic Graphs
Given a directed graph $G$ and integers $k$ and $l$, a D-core is the maximal subgraph $H \subseteq G$ such that for every vertex of $H$, its in-degree and out-degree are no smaller than $k$ and $l$, respectively. For a directed graph $G$,…
Expander decompositions of graphs have significantly advanced the understanding of many classical graph problems and led to numerous fundamental theoretical results. However, their adoption in practice has been hindered due to their…
We introduce a $k$-leaf removal algorithm as a generalization of the so-called leaf removal algorithm. In this pruning algorithm, vertices of degree smaller than $k$, together with their first nearest neighbors and all incident edges are…
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…
The densest $k$-subgraph problem is the problem of finding a $k$-vertex subgraph of a graph with the maximum number of edges. In order to solve large instances of the densest $k$-subgraph problem, we introduce two algorithms that are based…
Hypergraphs are a powerful abstraction for modeling high-order relations, which are ubiquitous in many fields. A hypergraph consists of nodes and hyperedges (i.e., subsets of nodes); and there have been a number of attempts to extend the…
(Hyper)Graph decomposition is a family of problems that aim to break down large (hyper)graphs into smaller sub(hyper)graphs for easier analysis. The importance of this lies in its ability to enable efficient computation on large and complex…
Neural networks are the pinnacle of Artificial Intelligence, as in recent years we witnessed many novel architectures, learning and optimization techniques for deep learning. Capitalizing on the fact that neural networks inherently…
We present a practically efficient algorithm for maintaining a global minimum cut in large dynamic graphs under both edge insertions and deletions. While there has been theoretical work on this problem, our algorithm is the first…
Clustering analysis has been widely used in trust evaluation on various complex networks such as wireless sensors networks and online social networks. Spectral clustering is one of the most commonly used algorithms for graph-structured data…
Graph classification is a pivotal challenge in machine learning, especially within the realm of graph-based data, given its importance in numerous real-world applications such as social network analysis, recommendation systems, and…
Densest subgraph discovery (DSD) is a fundamental problem in graph mining. It has been studied for decades, and is widely used in various areas, including network science, biological analysis, and graph databases. Given a graph G, DSD aims…
We study the NP-hard graph problem Collapsed k-Core where, given an undirected graph G and integers b, x, and k, we are asked to remove b vertices such that the k-core of remaining graph, that is, the (uniquely determined) largest induced…
We consider the (exact, minimum) $k$-cut problem: given a graph and an integer $k$, delete a minimum-weight set of edges so that the remaining graph has at least $k$ connected components. This problem is a natural generalization of the…
In order to support the real-time interaction with LLMs and the instant search or the instant recommendation on social media, it becomes an imminent problem to build a k-NN graph or an indexing graph for the massive number of vectorized…
We study the parameterized complexity of the Cograph Deletion problem, which asks whether one can delete at most $k$ edges from a graph to make it $P_4$-free. This is a well-known graph modification problem with applications in computation…
Motivated by the increasing need for fast processing of large-scale graphs, we study a number of fundamental graph problems in a message-passing model for distributed computing, called $k$-machine model, where we have $k$ machines that…
Community detection is expensive, and the cost generally depends at least linearly on the number of vertices in the graph. We propose working with a reduced graph that has many fewer nodes but nonetheless captures key community structure.…
The organisation of a network in a maximal set of nodes having at least $k$ neighbours within the set, known as $k$-core decomposition, has been used for studying various phenomena. It has been shown that nodes in the innermost $k$-shells…
Reconfigurable optical topologies promise to improve the performance in datacenters by dynamically optimizing the physical network in a demand-aware manner. State-of-the-art optical technologies allow to establish and update direct…