Related papers: Distance-preserving graph contractions
We show that large subsets of vector spaces over finite fields determine certain point configurations with prescribed distance structure. More specifically, we consider the complete graph with vertices as the points of $A \subseteq…
Graph algorithms are central to large-scale applications such as navigation systems, social networks, and data analysis platforms. This thesis studies two important challenges in such systems: robustness to failures and fairness in…
A spanning tree of a network or graph is a subgraph that connects all nodes with the least number or weight of edges. The spanning tree is one of the most straightforward techniques for network simplification and sampling, and for…
Hyperbolicity is a graph parameter which indicates how much the shortest-path distance metric of a graph deviates from a tree metric. It is used in various fields such as networking, security, and bioinformatics for the classification of…
The interconnectedness and interdependence of modern graphs are growing ever more complex, causing enormous resources for processing, storage, communication, and decision-making of these graphs. In this work, we focus on the task graph…
One of the important features of an interconnection network is its ability to efficiently simulate programs or parallel algorithms written for other architectures. Such a simulation problem can be mathematically formulated as a graph…
With applications in distribution systems and communication networks, the minimum stretch spanning tree problem is to find a spanning tree T of a graph G such that the maximum distance in T between two adjacent vertices is minimized. The…
For a given graph $\mathcal{G}$ of order $n$ with $m$ edges, and a real symmetric matrix associated to the graph, $M\left(\mathcal{G}\right)\in\mathbb{R}^{n\times n}$, the interlacing graph reduction problem is to find a graph…
Stress models are a promising approach for graph drawing. They minimize the weighted sum of the squared errors of the Euclidean and desired distances for each node pair. The desired distance typically uses the graph-theoretic distances…
We present a general toolbox, based on new vertex sparsifiers, for designing data structures to maintain shortest paths in dynamic graphs. In an $m$-edge graph undergoing edge insertions and deletions, our data structures give the first…
We study the problem of how well a tree metric is able to preserve the sum of pairwise distances of an arbitrary metric. This problem is closely related to low-stretch metric embeddings and is interesting by its own flavor from the line of…
We investigate the computation of minimum-cost spanning trees satisfying prescribed vertex degree constraints: Given a graph $G$ and a constraint function $D$, we ask for a (minimum-cost) spanning tree $T$ such that for each vertex $v$, $T$…
Graphs are central to modeling complex systems in domains such as social networks, molecular chemistry, and neuroscience. While Graph Neural Networks, particularly Graph Convolutional Networks, have become standard tools for graph learning,…
Network alignment is useful for multiple applications that require increasingly large graphs to be processed. Existing research approaches this as an optimization problem or computes the similarity based on node representations. However,…
The shrinking operation converts a hypergraph into a graph by choosing, from each hyperedge, two endvertices of a corresponding graph edge. A hypertree is a hypergraph which can be shrunk to a tree on the same vertex set. Klimo\v{s}ov\'{a}…
We consider the well-studied problem of finding a spanning tree with minimum average distance between vertex pairs (called a MAD tree). This is a classic network design problem which is known to be NP-hard. While approximation algorithms…
Graph clustering aims to partition nodes into distinct clusters based on their similarity, thereby revealing relationships among nodes. Nevertheless, most existing methods do not fully utilize these edge weights. Leveraging edge weights in…
Betweenness is a well-known centrality measure that ranks the nodes of a network according to their participation in shortest paths. Since an exact computation is prohibitive in large networks, several approximation algorithms have been…
To quantify the fundamental evolution of time-varying networks, and detect abnormal behavior, one needs a notion of temporal difference that captures significant organizational changes between two successive instants. In this work, we…
Fault tolerant distance preservers (spanners) are sparse subgraphs that preserve (approximate) distances between given pairs of vertices under edge or vertex failures. So-far, these structures have been studied mainly from a centralized…