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We consider the Survivable Network Design problem (SNDP) in the single-pass insertion-only streaming model. The input to SNDP is an edge-weighted graph $G = (V, E)$ and an integer connectivity requirement $r(uv)$ for each $u, v \in V$. The…
Vertex splitting is a graph operation that replaces a vertex $v$ with two nonadjacent new vertices and makes each neighbor of $v$ adjacent with one or both of the introduced vertices. Vertex splitting has been used in contexts from circuit…
Mobile edge computing is a new cloud computing paradigm which makes use of small-sized edge-clouds to provide real-time services to users. These mobile edge-clouds (MECs) are located in close proximity to users, thus enabling users to…
In this article, we consider the Virtual Network Embedding (VNE) problem for 5G networks slicing. This problem requires to allocate multiple Virtual Networks (VN) on a substrate virtualized physical network while maximizing among others,…
Given an input graph G and a node v in G, homogeneous network embedding (HNE) maps the graph structure in the vicinity of v to a compact, fixed-dimensional feature vector. This paper focuses on HNE for massive graphs, e.g., with billions of…
In the Vector Connectivity problem we are given an undirected graph $G=(V,E)$, a demand function $\phi\colon V\to\{0,\ldots,d\}$, and an integer $k$. The question is whether there exists a set $S$ of at most $k$ vertices such that every…
In machine learning, graph embedding algorithms seek low-dimensional representations of the input network data, thereby allowing for downstream tasks on compressed encodings. Recently, within the framework of network renormalization,…
Virtual Network Embedding (VNE) is a technique for mapping virtual networks onto a physical network infrastructure, enabling multiple virtual networks to coexist on a shared physical network. Previous works focused on implementing…
Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its…
Graph matching can be formalized as a combinatorial optimization problem, where there are corresponding relationships between pairs of nodes that can be represented as edges. This problem becomes challenging when there are potential…
We consider the parametric reachability problem (PRP) for families of networks described by vertex-replacement (VR) graph grammars, where network nodes run replicas of finite-state processes that communicate via binary handshaking. We show…
Near ubiquitous mobile computing has led to intense interest in dynamic graph theory. This provides a new and challenging setting for algorithmics and complexity theory. For any graph-based problem, the rapid evolution of a (possibly…
In the classical Node-Disjoint Paths (NDP) problem, we are given an $n$-vertex graph $G=(V,E)$, and a collection $M=\{(s_1,t_1),\ldots,(s_k,t_k)\}$ of pairs of its vertices, called source-destination, or demand pairs. The goal is to route…
Steiner Tree Problem (STP) in graphs aims to find a tree of minimum weight in the graph that connects a given set of vertices. It is a classic NP-hard combinatorial optimization problem and has many real-world applications (e.g., VLSI chip…
Graph embedding learns low-dimensional representations for nodes in a graph and effectively preserves the graph structure. Recently, a significant amount of progress has been made toward this emerging research area. However, there are…
Virtualization facilitates heterogeneous cloud applications to share the same physical infrastructure with admirable flexibility, while resource efficiency and survivability are critical concerns for virtual network embedding (VNE). As more…
Measuring similarity between IP addresses is an important task in the daily operations of any enterprise network. Applications that depend on an IP similarity measure include measuring correlation between security alerts, building baselines…
Networks are inherently vulnerable to vertex failures, making the analysis of their structural robustness a fundamental problem in graph theory. In this study, we investigate the closeness and vertex residual closeness of graphs, with a…
Robust optimization is concerned with constructing solutions that remain feasible also when a limited number of resources is removed from the solution. Most studies of robust combinatorial optimization to date made the assumption that every…
Effective traffic prediction is a cornerstone of intelligent transportation systems, enabling precise forecasts of traffic flow, speed, and congestion. While traditional spatio-temporal graph neural networks (ST-GNNs) have achieved notable…