Related papers: Multistage Graph Problems on a Global Budget
Graph neural networks have shown to learn effective node representations, enabling node-, link-, and graph-level inference. Conventional graph networks assume static relations between nodes, while relations between entities in a video often…
Treewidth is arguably the most important structural graph parameter leading to algorithmically beneficial graph decompositions. Triggered by a strongly growing interest in temporal networks (graphs where edge sets change over time), we…
Addressing a quest by Gupta et al. [ICALP'14], we provide a first, comprehensive study of finding a short s-t path in the multistage graph model, referred to as the Multistage s-t Path problem. Herein, given a sequence of graphs over the…
This work proposes an algorithmic framework to learn time-varying graphs from online data. The generality offered by the framework renders it model-independent, i.e., it can be theoretically analyzed in its abstract formulation and then…
Most transportation networks are inherently temporal: Connections (e.g. flights, train runs) are only available at certain, scheduled times. When transporting passengers or commodities, this fact must be considered for the the planning of…
Given an undirected graph $G$, the problem of deciding whether $G$ admits a simple and proper time-labeling that makes it temporally connected is known to be NP-hard (G\"obel et al., 1991). In this article, we relax this problem and ask…
The VertexCover problem is proven to be computationally hard in different ways: It is NP-complete to find an optimal solution and even NP-hard to find an approximation with reasonable factors. In contrast, recent experiments suggest that on…
The problem of finding paths in temporal graphs has been recently considered due to its many applications. In this paper we consider a variant of the problem that, given a vertex-colored temporal graph, asks for a path whose vertices have…
Over the years, many multiprocessor locking protocols have been designed and analyzed. However, the performance of these protocols highly depends on how the tasks are partitioned and prioritized and how the resources are shared locally and…
Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…
Neural networks that compute over graph structures are a natural fit for problems in a variety of domains, including natural language (parse trees) and cheminformatics (molecular graphs). However, since the computation graph has a different…
The independent set on a graph $G=(V,E)$ is a subset of $V$ such that no two vertices in the subset have an edge between them. The MIS problem on $G$ seeks to identify an independent set with maximum cardinality, i.e. maximum independent…
Temporal graphs have edge sets that change over discrete time steps. Such graphs are temporally connected (TC) if all pairs of vertices can reach each other using paths that traverse the edges in a time-respecting way (temporal paths).…
Recent progress in research on Deep Graph Networks (DGNs) has led to a maturation of the domain of learning on graphs. Despite the growth of this research field, there are still important challenges that are yet unsolved. Specifically,…
The problem Level Planarity asks for a crossing-free drawing of a graph in the plane such that vertices are placed at prescribed y-coordinates (called levels) and such that every edge is realized as a y-monotone curve. In the variant…
Graphs may be used to represent many different problem domains -- a concrete example is that of detecting communities in social networks, which are represented as graphs. With big data and more sophisticated applications becoming widespread…
We consider the problem of finding a 1-planar drawing for a general graph, where a 1-planar drawing is a drawing in which each edge participates in at most one crossing. Since this problem is known to be NP-hard we investigate the…
In recent years, there has been a surge in the prevalence of high- and multi-dimensional temporal data across various scientific disciplines. These datasets are characterized by their vast size and challenging potential for analysis. Such…
The P versus NP problem asks whether every language verifiable in polynomial time can also be decided in deterministic polynomial time. In this paper, we present a constructive proof that P = NP by introducing a universal, graph-based…
The world is dynamic and changes over time, thus any optimization problem used to model real life problems must address this dynamic nature, taking into account the cost of changes to a solution over time. The multistage model was…