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The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been…
The graph isomorphism problem looks deceptively simple, but although polynomial-time algorithms exist for certain types of graphs such as planar graphs and graphs with bounded degree or eigenvalue multiplicity, its complexity class is still…
Deep neural networks have been applied to a wide range of problems across different application domains with great success. Recently, research into combinatorial optimization problems in particular has generated much interest in the machine…
Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields…
We analyse the performance of simple distributed colouring algorithms under the assumption that the input graph is a hyperbolic random graph (HRG), a generative model capturing key properties of real-world networks such as power-law degree…
Recent works on machine learning for combinatorial optimization have shown that learning based approaches can outperform heuristic methods in terms of speed and performance. In this paper, we consider the problem of finding an optimal…
We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…
A common way to accelerate shortest path algorithms on graphs is the use of a bidirectional search, which simultaneously explores the graph from the start and the destination. It has been observed recently that this strategy performs…
We present a simple deterministic distributed algorithm that computes a $(\Delta+1)$-vertex coloring in $O(\log^2 \Delta \cdot \log n)$ rounds. The algorithm can be implemented with $O(\log n)$-bit messages. The algorithm can also be…
A maximum priority matching is a matching in an undirected graph that maximizes a priority score defined with respect to given vertex priorities. An earlier paper showed how to find maximum priority matchings in unweighted graphs. This…
Seminal works on graph neural networks have primarily targeted semi-supervised node classification problems with few observed labels and high-dimensional signals. With the development of graph networks, this setup has become a de facto…
We present the first (randomized) parallel dynamic algorithm for maximal matching, which can process an arbitrary number of updates simultaneously. Given a batch of edge deletion or insertion updates to the graph, our parallel algorithm…
We present the first data structures that maintain near optimal maximum cardinality and maximum weighted matchings on sparse graphs in sublinear time per update. Our main result is a data structure that maintains a $(1+\epsilon)$…
Consider the following simple coloring algorithm for a graph on $n$ vertices. Each vertex chooses a color from $\{1, \dotsc, \Delta(G) + 1\}$ uniformly at random. While there exists a conflicted vertex choose one such vertex uniformly at…
Dynamic graphs model many real-world applications, and as their sizes grow, efficiently storing and updating them becomes critical. We present RadixGraph, a fast and memory-efficient data structure for dynamic graph storage. RadixGraph…
The vast amounts of data used in social, business or traffic networks, biology and other natural sciences are often managed in graph-based data sets, consisting of a few thousand up to billions and trillions of vertices and edges,…
A hypergraph is a useful combinatorial object to model ternary or higher-order relations among entities. Clustering hypergraphs is a fundamental task in network analysis. In this study, we develop two clustering algorithms based on…
We present a new approach to randomized distributed graph coloring that is simpler and more efficient than previous ones. In particular, it allows us to tackle the $(\operatorname{deg}+1)$-list-coloring (D1LC) problem, where each node $v$…
Dense subgraph extraction is a fundamental problem in graph analysis and data mining, aimed at identifying cohesive and densely connected substructures within a given graph. It plays a crucial role in various domains, including social…
Recently bipartite graphs have been widely used to represent the relationship two sets of items for information retrieval applications. The Web offers a wide range of data which can be represented by bipartite graphs, such us movies and…