Related papers: Computing Maximum Matchings in Temporal Graphs
Eternal vertex cover problem is a variant of the classical vertex cover problem modeled as a two player attacker-defender game. Computing eternal vertex cover number of graphs is known to be NP-hard in general and the complexity status of…
Multiple interval graphs are variants of interval graphs where instead of a single interval, each vertex is assigned a set of intervals on the real line. We study the complexity of the MAXIMUM CLIQUE problem in several classes of multiple…
A \emph{Temporal Network} (also known as \emph{Link Stream} or \emph{Time-Varying Graph}) is often used to model a time-varying relationship among a group of agents. It is typically represented as a collection of triplets of the form…
The MEG (minimum equivalent graph) problem is, given a directed graph, to find a small subset of the edges that maintains all reachability relations between nodes. The problem is NP-hard. This paper gives a proof that, for graphs where each…
Graphs are becoming one of the most popular data modeling paradigms since they are able to model complex relationships that cannot be easily captured using traditional data models. One of the major tasks of graph management is graph…
Here we prove that counting maximum matchings in planar, bipartite graphs is #P-complete. This is somewhat surprising in the light that the number of perfect matchings in planar graphs can be computed in polynomial time. We also prove that…
Signal processing and machine learning algorithms for data supported over graphs, require the knowledge of the graph topology. Unless this information is given by the physics of the problem (e.g., water supply networks, power grids), the…
We present two deterministic dynamic algorithms for the maximum matching problem. (1) An algorithm that maintains a $(2+\epsilon)$-approximate maximum matching in general graphs with $O(\text{poly}(\log n, 1/\epsilon))$ update time. (2) An…
In this work, we introduce a filtration on temporal graphs based on $\delta$-temporal motifs (recurrent subgraphs), yielding a multi-scale representation of temporal structure. Our temporal filtration allows tools developed for filtered…
Detecting anomalous edges in dynamic graphs is an important task in many applications over evolving triple-based data, such as social networks, transaction management, and epidemiology. A major challenge with this task is the absence of…
A planar orthogonal drawing {\Gamma} of a connected planar graph G is a geometric representation of G such that the vertices are drawn as distinct points of the plane, the edges are drawn as chains of horizontal and vertical segments, and…
We propose a node clustering method for time-varying graphs based on the assumption that the cluster labels are changed smoothly over time. Clustering is one of the fundamental tasks in many science and engineering fields including signal…
The graph matching problem emerges naturally in various applications such as web privacy, image processing and computational biology. In this paper, graph matching is considered under a stochastic model, where a pair of randomly generated…
A temporal graph is a graph whose edges appear only at certain points in time. Recently, the second and the last three authors proposed a natural temporal analog of the Erd\H{o}s-R\'enyi random graph model. The proposed model is obtained by…
Node connectivity plays a central role in temporal network analysis. We provide a comprehensive study of various concepts of walks in temporal graphs, that is, graphs with fixed vertex sets but edge sets changing over time. Taking into…
We consider the algorithmic complexity of recognizing bipartite temporal graphs. Rather than defining these graphs solely by their underlying graph or individual layers, we define a bipartite temporal graph as one in which every layer can…
Temporal information is increasingly available as part of large network data sets. This information reveals sequences of link activations between network entities, which can expose underlying processes in the data. Examples include the…
In a recent paper, we introduced the simultaneous representation problem (defined for any graph class C) and studied the problem for chordal, comparability and permutation graphs. For interval graphs, the problem is defined as follows. Two…
Cohesive subgraph mining is a fundamental problem in bipartite graph analysis. In reality, relationships between two types of entities often occur at some specific timestamps, which can be modeled as a temporal bipartite graph. However, the…
The study of time-varying (dynamic) networks (graphs) is of fundamental importance for computer network analytics. Several methods have been proposed to detect the effect of significant structural changes in a time series of graphs. The…