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We consider a generic algorithmic paradigm that we call progressive exploration, which can be used to develop simple and efficient parameterized graph algorithms. We identify two model-theoretic properties that lead to efficient progressive…

We consider a class of growing random graphs obtained by creating vertices sequentially one by one: at each step, we choose uniformly the neighbours of the newly created vertex; its degree is a random variable with a fixed but arbitrary…

In this paper, we address a class of specially structured problems that include speed planning, for mobile robots and robotic manipulators, and dynamic programming. We develop two new numerical procedures, that apply to the general case and…

Understanding what graph neural networks can learn, especially their ability to learn to execute algorithms, remains a central theoretical challenge. In this work, we prove exact learnability results for graph algorithms under…

Typical performance of approximation algorithms is studied for randomized minimum vertex cover problems. A wide class of random graph ensembles characterized by an arbitrary degree distribution is discussed with some theoretical frameworks.…

We give an explicit construction of the weak local limit of a class of preferential attachment graphs. This limit contains all local information and allows several computations that are otherwise hard, for example, joint degree…

We resolve a number of long-standing open problems in online graph coloring. More specifically, we develop tight lower bounds on the performance of online algorithms for fundamental graph classes. An important contribution is that our…

We provide a novel approach to construct generative models for graphs. Instead of using the traditional probabilistic models or deep generative models, we propose to instead find an algorithm that generates the data. We achieve this using…

This paper provides an algorithmic framework for obtaining fast distributed algorithms for a highly-dynamic setting, in which *arbitrarily many* edge changes may occur in each round. Our algorithm significantly improves upon prior work in…

The present paper studies local distributed graph problems in highly dynamic networks. Communication and changes of the graph happen in synchronous rounds and our algorithms always, i.e., in every round, satisfy non-trivial guarantees, no…

The generation of random graphs using edge swaps provides a reliable method to draw uniformly random samples of sets of graphs respecting some simple constraints, e.g. degree distributions. However, in general, it is not necessarily…

We show a deterministic constant-time local algorithm for constructing an approximately maximum flow and minimum fractional cut in multisource-multitarget networks with bounded degrees and bounded edge capacities. Locality means that the…

We propose a wide class of preferential attachment models of random graphs, generalizing previous approaches. Graphs described by these models obey the power-law degree distribution, with the exponent that can be controlled in the models.…

Local thresholding algorithms were first presented more than a decade ago and have since been applied to a variety of data mining tasks in peer-to-peer systems, wireless sensor networks, and in grid systems. One critical assumption made by…

We use probabilistic methods to find lower bounds on the maximum number, in a graph with domination number \gamma, of dominating sets of size \gamma. We find that we can randomly generate a graph that, w.h.p., is dominated by almost all…

In this paper, we hope to bring closer graph theory and consensus algorithms. Firstly, we give a brief introduction to graph theory by listing a concise definition. Then we analyze and visualize some commonly used graphs. Secondly, we…

Learning embeddings from large-scale networks is an open challenge. Despite the overwhelming number of existing methods, is is unclear how to exploit network structure in a way that generalizes easily to unseen nodes, edges or graphs. In…

A class of random graph models is considered, combining features of exponential-family models and latent structure models, with the goal of retaining the strengths of both of them while reducing the weaknesses of each of them. An open…

We show that there is a deterministic local algorithm (constant-time distributed graph algorithm) that finds a 5-approximation of a minimum dominating set on outerplanar graphs. We show there is no such algorithm that finds a…

Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…