Related papers: Making Temporal Betweenness Computation Faster and…
Modularity is a very widely used measure of the level of clustering or community structure in networks. Here we consider a recent generalisation of the definition of modularity to temporal graphs, whose edge-sets change over discrete…
A class of centrality measures called betweenness centralities reflects degree of participation of edges or nodes in communication between different parts of the network. The original shortest-path betweenness centrality is based on…
Connectivity (or equivalently, unweighted maximum flow) is an important measure in graph theory and combinatorial optimization. Given a graph $G$ with vertices $s$ and $t$, the connectivity $\lambda(s,t)$ from $s$ to $t$ is defined to be…
Most networks are not static objects, but instead they change over time. This observation has sparked rigorous research on temporal graphs within the last years. In temporal graphs, we have a fixed set of nodes and the connections between…
A temporal graph has an edge set that may change over discrete time steps, and a temporal path (or walk) must traverse edges that appear at increasing time steps. Accordingly, two temporal paths (or walks) are temporally disjoint if they do…
We consider the fundamental problems of determining the rooted and global edge and vertex connectivities (and computing the corresponding cuts) in directed graphs. For rooted (and hence also global) edge connectivity with small integer…
In recent years the Cache-Oblivious model of external memory computation has provided an attractive theoretical basis for the analysis of algorithms on massive datasets. Much progress has been made in discovering algorithms that are…
A temporal graph is a dynamic graph where every edge is assigned a set of integer time labels that indicate at which discrete time step the edge is available. In this paper, we study how changes of the time labels, corresponding to delays…
Consider the following distance query for an $n$-node graph $G$ undergoing edge insertions and deletions: given two sets of nodes $I$ and $J$, return the distances between every pair of nodes in $I\times J$. This query is rather general and…
We study the problem of computing all Pareto-optimal journeys in a public transit network regarding the two criteria of arrival time and number of transfers taken. We take a novel approach, focusing on trips and transfers between them,…
On sparse graphs, Roditty and Williams [2013] proved that no $O(n^{2-\varepsilon})$-time algorithm achieves an approximation factor smaller than $\frac{3}{2}$ for the diameter problem unless SETH fails. In this article, we solve an open…
The betweenness centrality of graphs using random walk paths instead of geodesics is studied. A scaling collapse with no adjustable parameters is obtained as the graph size $N$ is varied; the scaling curve depends on the graph model. A…
A shortest-path algorithm finds a path containing the minimal cost between two vertices in a graph. A plethora of shortest-path algorithms is studied in the literature that span across multiple disciplines. This paper presents a survey of…
We show that many classical optimization problems --- such as $(1\pm\epsilon)$-approximate maximum flow, shortest path, and transshipment --- can be computed in $\newcommand{\tmix}{{\tau_{\text{mix}}}}\tmix(G)\cdot n^{o(1)}$ rounds of…
We give a deterministic algorithm for computing a global minimum vertex cut in a vertex-weighted graph $n$ vertices and $m$ edges in $\widehat O(mn)$ time. This breaks the long-standing $\widehat \Omega(n^{4})$-time barrier in dense graphs,…
We study tensor networks as a model of arithmetic computation for evaluating multilinear maps. These capture any algorithm based on low border rank tensor decompositions, such as $O(n^{\omega+\epsilon})$ time matrix multiplication, and in…
Temporal graphs represent graph evolution over time, and have been receiving considerable research attention. Work on expressing temporal graph patterns or discovering temporal motifs typically assumes relatively simple temporal…
Group interactions arise in our daily lives (email communications, on-demand ride sharing, comment interactions on online communities, to name a few), and they together form hypergraphs that evolve over time. Given such temporal…
In this paper, we propose a randomized $\tilde{O}(\mu(G))$-round algorithm for the maximum cardinality matching problem in the CONGEST model, where $\mu(G)$ means the maximum size of a matching of the input graph $G$. The proposed algorithm…
In this paper, we propose an online algorithm mspace for forecasting node features in temporal graphs, which captures spatial cross-correlation among different nodes as well as the temporal auto-correlation within a node. The algorithm can…