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Operators of reconfigurable wavelength-division multiplexed (WDM) optical networks adapt the lightpath topology to balance load and reduce transmission delays. Such an adaption generally depends on a known or estimated traffic matrix.…
The Weighted Tree Augmentation problem (WTAP) is a fundamental problem in network design. In this paper, we consider this problem in the online setting. We are given an $n$-vertex spanning tree $T$ and an additional set $L$ of edges (called…
Tree projections provide a unifying framework to deal with most structural decomposition methods of constraint satisfaction problems (CSPs). Within this framework, a CSP instance is decomposed into a number of sub-problems, called views,…
In this paper, we study the problem of finding a minimum weight spanning tree that contains each vertex in a given subset $V_{\rm NT}$ of vertices as an internal vertex. This problem, called Minimum Weight Non-Terminal Spanning Tree,…
Mobile edge computing offers a myriad of opportunities to innovate and introduce novel applications, thereby enhancing user experiences considerably. A critical issue extensively investigated in this domain is efficient deployment of…
The contraction cost of a tensor network depends on the contraction order. However, the optimal contraction ordering problem is known to be NP-hard. We show that the linear contraction ordering problem for tree tensor networks admits a…
Querying the shortest path between two vertexes is a fundamental operation in a variety of applications, which has been extensively studied over static road networks. However, in reality, the travel costs of road segments evolve over time,…
While much of network design focuses mostly on cost (number or weight of edges), node degrees have also played an important role. They have traditionally either appeared as an objective, to minimize the maximum degree (e.g., the Minimum…
Network embedding has recently emerged as a promising technique to embed nodes of a network into low-dimensional vectors. While fairly successful, most existing works focus on the embedding techniques for static networks. But in practice,…
Link prediction, as a frontier task in complex network topology analysis, aims to infer the existence of latent links between node pairs based on observed nodes and structural information. We propose an ensemble link prediction model that…
It is well-known that cloud application performance critically depends on the network. Accordingly, new abstractions for cloud applications are proposed which extend the performance isolation guarantees to the network. The most common…
This tutorial covers a few recent papers in the field of network embedding. Network embedding is a collective term for techniques for mapping graph nodes to vectors of real numbers in a multidimensional space. To be useful, a good embedding…
Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
Finding optimal matchings in dense graphs is of general interest and of particular importance in social, transportation and biological networks. While developing optimal solutions for various matching problems is important, the running…
Node2vec is a graph embedding method that learns a vector representation for each node of a weighted graph while seeking to preserve relative proximity and global structure. Numerical experiments suggest Node2vec struggles to recreate the…
Tensor networks provide a powerful framework for compressing multi-dimensional data. The optimal tensor network structure for a given data tensor depends on both data characteristics and specific optimality criteria, making tensor network…
In the Steiner Tree Augmentation Problem (STAP), we are given a graph $G = (V,E)$, a set of terminals $R \subseteq V$, and a Steiner tree $T$ spanning $R$. The edges $L := E \setminus E(T)$ are called links and have non-negative costs. The…
Embeddings of graphs into distributions of trees that preserve distances in expectation are a cornerstone of many optimization algorithms. Unfortunately, online or dynamic algorithms which use these embeddings seem inherently randomized and…
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…