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Metric graphs are structures obtained by associating edges in a standard graph with segments of the real line and gluing these segments at the vertices of the graph. The resulting structure has a natural metric that allows for the study of…
We derive new discrete event simulation algorithms for marked time point processes. The main idea is to couple a special structure, namely the associated local independence graph, as defined by Didelez arXiv:0710.5874, with the activity…
We study the potential utility of classical techniques of spectral sparsification of graphs as a preprocessing step for digital quantum algorithms, in particular, for Hamiltonian simulation. Our results indicate that spectral sparsification…
A new efficient algorithm is presented for finding all simple cycles that satisfy a length constraint in a directed graph. When the number of vertices is non-trivial, most cycle-finding problems are of practical interest for sparse graphs…
For an arbitrary initial configuration of discrete loads over vertices of a distributed graph, we consider the problem of minimizing the {\em discrepancy} between the maximum and minimum loads among all vertices. For this problem, this…
We present new, more efficient algorithms for estimating random walk scores such as Personalized PageRank from a given source node to one or several target nodes. These scores are useful for personalized search and recommendations on…
We study the problem of finding the maximum of a function defined on the nodes of a connected graph. The goal is to identify a node where the function obtains its maximum. We focus on local iterative algorithms, which traverse the nodes of…
In a coalescing random walk, a set of particles make independent random walks on a graph. Whenever one or more particles meet at a vertex, they unite to form a single particle, which then continues the random walk through the graph.…
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links.…
We study deterministic algorithms for computing graph cuts, with focus on two fundamental problems: balanced sparse cut and $k$-vertex connectivity for small $k$ ($k=O(\polylog n)$). Both problems can be solved in near-linear time with…
We describe a new family of $k$-uniform hypergraphs with independent random edges. The hypergraphs have a high probability of being peelable, i.e. to admit no sub-hypergraph of minimum degree $2$, even when the edge density (number of edges…
An important part of many machine learning workflows on graphs is vertex representation learning, i.e., learning a low-dimensional vector representation for each vertex in the graph. Recently, several powerful techniques for unsupervised…
Kemeny's constant measures how fast a random walker moves around in a graph. Expressions for Kemeny's constant can be quite involved, and for this reason, many lines of research focus on graphs with structure that makes them amenable to…
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…
In the decremental single-source shortest paths (SSSP) problem we want to maintain the distances between a given source node $s$ and every other node in an $n$-node $m$-edge graph $G$ undergoing edge deletions. While its static counterpart…
Recently, random walks on dynamic graphs have been studied because of their adaptivity to the time-varying structure of real-world networks. In general, there is a tremendous gap between static and dynamic graph settings for the lazy simple…
We study dynamic graph algorithms in the Massively Parallel Computation model, which was inspired by practical data processing systems. Our goal is to provide algorithms that can efficiently handle large batches of edge insertions and…
We consider an elementary model for self-organised criticality, the activated random walk on the complete graph. We introduce a discrete time Markov chain as follows. At each time step, we add an active particle at a random vertex and let…
The training of graph neural networks (GNNs) is extremely time consuming because sparse graph-based operations are hard to be accelerated by hardware. Prior art explores trading off the computational precision to reduce the time complexity…
We study the efficient generation of random graphs with a prescribed expected degree sequence, focusing on rank-1 inhomogeneous models in which vertices are assigned weights and edges are drawn independently with probabilities proportional…