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Graphs are ubiquitous due to their flexibility in representing social and technological systems as networks of interacting elements. Graph representation learning methods, such as node embeddings, are powerful approaches to map nodes into a…
A graph $G$ is a \emph{max point-tolerance (MPT)} graph if each vertex $v$ of $G$ can be mapped to a \emph{pointed-interval} $(I_v, p_v)$ where $I_v$ is an interval of $\mathbb{R}$ and $p_v \in I_v$ such that $uv$ is an edge of $G$ iff $I_u…
Flexible network design deals with building a network that guarantees some connectivity requirements between its vertices, even when some of its elements (like vertices or edges) fail. In particular, the set of edges (resp. vertices) of a…
For any undirected graph $G=(V,E)$ and a set $E_W$ of candidate edges with $E\cap E_W=\emptyset$, the $(k,\gamma)$-spectral augmentability problem is to find a set $F$ of $k$ edges from $E_W$ with appropriate weighting, such that the…
Networks have become indispensable and ubiquitous structures in many fields to model the interactions among different entities, such as friendship in social networks or protein interactions in biological graphs. A major challenge is to…
Given a graph G where each node is associated with a set of attributes, attributed network embedding (ANE) maps each node v in G to a compact vector Xv, which can be used in downstream machine learning tasks. Ideally, Xv should capture node…
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…
Graph matching refers to finding node correspondence between graphs, such that the corresponding node and edge's affinity can be maximized. In addition with its NP-completeness nature, another important challenge is effective modeling of…
Rigidity theory studies the properties of graphs that can have rigid embeddings in a euclidean space $\mathbb{R}^d$ or on a sphere and which in addition satisfy certain edge length constraints. One of the major open problems in this field…
The increasing demand for diverse emerging applications has resulted in the interconnection of multi-access edge computing (MEC) systems via metro optical networks. To cater to these diverse applications, network slicing has become a…
To fully exploit the performance potential of modern multi-core processors, machine learning and data mining algorithms for big data must be parallelized in multiple ways. Today's CPUs consist of multiple cores, each following an…
We propose a novel optimization-based approach to embedding heterogeneous high-dimensional data characterized by a graph. The goal is to create a two-dimensional visualization of the graph structure such that edge-crossings are minimized…
We revisit the issue of low-distortion embedding of metric spaces into the line, and more generally, into the shortest path metric of trees, from the parameterized complexity perspective.Let $M=M(G)$ be the shortest path metric of an edge…
This work presents a machine learning approach to optimize the energy efficiency (EE) in a multi-cell wireless network. This optimization problem is non-convex and its global optimum is difficult to find. In the literature, either simple…
The Multimarginal Schr\"odinger Bridge (MSB) finds the optimal coupling among a collection of random vectors with known statistics and a known correlation structure. In the MSB formulation, this correlation structure is specified \emph{a…
Network virtualization (NV) is a technology with broad application prospects. Virtual network embedding (VNE) is the core orientation of VN, which aims to provide more flexible underlying physical resource allocation for user function…
We derive a new lower bound for the bandwidth of a graph that is based on a new lower bound for the minimum cut problem. Our new semidefinite programming relaxation of the minimum cut problem is obtained by strengthening the known…
We introduce Multivariate Multiscale Graph-based Dispersion Entropy (mvDEG), a novel, computationally efficient method for analyzing multivariate time series data in graph and complex network frameworks, and demonstrate its application in…
Given an undirected node-weighted graph, the Maximum-Weight Connected Subgraph problem (MWCS) is to identify a subset of nodes of maximalsum of weights that induce a connected subgraph. MWCS is closely related to the well-studied Prize…
Network virtualization provides a promising solution to overcome the ossification of current networks, allowing multiple Virtual Network Requests (VNRs) embedded on a common infrastructure. The major challenge in network virtualization is…