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Unsupervised feature learning often finds low-dimensional embeddings that capture the structure of complex data. For tasks for which prior expert topological knowledge is available, incorporating this into the learned representation may…
We study the complexity of fundamental distributed graph problems in the recently popular setting where information about the input graph is available to the nodes before the start of the computation. We focus on the most common such…
A communication network can be modeled as a directed connected graph with edge weights that characterize performance metrics such as loss and delay. Network tomography aims to infer these edge weights from their pathwise versions measured…
Given an $n$-vertex non-negatively real-weighted graph $G$, whose vertices are partitioned into a set of $k$ clusters, a \emph{clustered network design problem} on $G$ consists of solving a given network design optimization problem on $G$,…
In this work, a graph partitioning problem in a fixed number of connected components is considered. Given an undirected graph with costs on the edges, the problem consists of partitioning the set of nodes into a fixed number of subsets with…
The robust topology optimization formulation that introduces the eroded and dilated versions of the design has gained increasing popularity in recent years, mainly because of its ability to produce designs satisfying a minimum length scale.…
Network embedding assigns nodes in a network to low-dimensional representations and effectively preserves the network structure. Recently, a significant amount of progresses have been made toward this emerging network analysis paradigm. In…
A metric graph is a 1-dimensional stratified metric space consisting of vertices and edges or loops glued together. Metric graphs can be naturally used to represent and model data that take the form of noisy filamentary structures, such as…
In this paper, we consider the minimum spanning tree problem (for short, MSTP) on an arbitrary set of $n$ points of $d$-dimensional space in $l_1$-norm. For this problem, for each fixed $d\geq 2$, there is a known algorithm of the…
We study the problem of finding a minimum-distortion embedding of the shortest path metric of an unweighted graph into a "simpler" metric $X$. Computing such an embedding (exactly or approximately) is a non-trivial task even when $X$ is the…
Network embedding is an effective method to learn low-dimensional representations of nodes, which can be applied to various real-life applications such as visualization, node classification, and link prediction. Although significant…
In the paper we consider the linear underdetermined system of a special type. Systems of this type appear in non-homogeneous network flow programming problems in the form of systems of constraints and can be characterized as systems with a…
In this work, we consider the problem of placing replicas in a data center or storage area network, represented as a digraph, so as to lexico-minimize a previously proposed reliability measure which minimizes the impact of all failure…
This thesis consists of two topics related to computational geometry and one topic related to topological data analysis (TDA), which combines fields of computational geometry and algebraic topology for analyzing data. The first part studies…
Successful machine learning on graphs or networks requires embeddings that not only represent nodes and edges as low-dimensional vectors but also preserve the graph structure. Established methods for generating embeddings require flexible…
Node embedding learns a low-dimensional representation for each node in the graph. Recent progress on node embedding shows that proximity matrix factorization methods gain superb performance and scale to large graphs with millions of nodes.…
Multilayer network analysis has become a vital tool for understanding different relationships and their interactions in a complex system, where each layer in a multilayer network depicts the topological structure of a group of nodes…
We consider the NP-hard Tree Containment problem that has important applications in phylogenetics. The problem asks if a given leaf-labeled network contains a subdivision of a given leaf-labeled tree. We develop a fast algorithm for the…
Problems in scientific computing, such as distributing large sparse matrix operations, have analogous formulations as hypergraph partitioning problems. A hypergraph is a generalization of a traditional graph wherein "hyperedges" may connect…
Graph embeddings play a significant role in the design and analysis of parallel algorithms. It is a mapping of the topological structure of a guest graph G into a host graph H, which is represented as a one-to-one mapping from the vertex…