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A $k$-spanner of a graph $G$ is a sparse subgraph that preserves its shortest path distances up to a multiplicative stretch factor of $k$, and a $k$-emulator is similar but not required to be a subgraph of $G$. A classic theorem by Thorup…
Using fault-tolerant constructions, computations performed with unreliable components can simulate their noiseless counterparts though the introduction of a modest amount of redundancy. Given the modest overhead required to achieve…
Analyzing the stability of graph neural networks (GNNs) under topological perturbations is key to understanding their transferability and the role of each architecture component. However, stability has been investigated only for particular…
With the increasing scale of communication networks, the likelihood of failures grows as well. Since these networks form a critical backbone of our digital society, it is important that they rely on robust routing algorithms which ensure…
Many complex systems, such as communication networks, display a surprising degree of robustness: while key components regularly malfunction, local failures rarely lead to the loss of the global information-carrying ability of the network.…
The reassembling of a simple connected graph G = (V,E) is an abstraction of a problem arising in earlier studies of network analysis. The reassembling process has a simple formulation (there are several equivalent formulations) relative to…
Mutual exclusion is one of the most commonly used techniques to handle contention in concurrent systems. Traditionally, mutual exclusion algorithms have been designed under the assumption that a process does not fail while…
Distributed storage systems in the presence of a wiretapper are considered. A distributed storage system (DSS) is parameterized by three parameters (n, k,d), in which a file stored across n distributed nodes, can be recovered from any k out…
The enhanced Bayesian network (eBN) methodology described in the companion paper facilitates the assessment of reliability and risk of engineering systems when information about the system evolves in time. We present the application of the…
This paper introduces a new class of efficient inter connection networks called as M-graphs for large multi-processor systems.The concept of M-matrix and M-graph is an extension of Mn-matrices and Mn-graphs.We analyze these M-graphs…
Structural balance theory studies stability in networks. Given a $n$-vertex complete graph $G=(V,E)$ whose edges are labeled positive or negative, the graph is considered \emph{balanced} if every triangle either consists of three positive…
Protective relays can mal-operate for transmission lines connected to doubly fed induction generator (DFIG) based large capacity wind farms (WFs). The performance of distance relays protecting such lines is investigated and a statistical…
To enhance robustness of complex networked systems, a simple method is introducing reinforced nodes which always function during failure propagation. A random scheme of node reinforcement can be considered as a benchmark for finding an…
We identify a trade-off between robustness and accuracy that serves as a guiding principle in the design of defenses against adversarial examples. Although this problem has been widely studied empirically, much remains unknown concerning…
Federated learning (FL) has emerged as a transformative paradigm for edge intelligence, enabling collaborative model training while preserving data privacy across distributed personal devices. However, the inherent volatility of edge…
Bayesian network models (Erdos Renyi, stochastic block models, random dot product graphs, graphons) are widely used in neuroscience, epidemiology, and the social sciences, yet real networks are sparse, heterogeneous, and exhibit…
Spanners are fundamental graph structures that sparsify graphs at the cost of small stretch. In particular, in recent years, many sequential algorithms constructing additive all-pairs spanners were designed, providing very sparse…
A distributed directory is an overlay data structure on a graph $G$ that helps to access a shared token $t$. The directory supports three operations: publish, to announce the token, lookup, to read the contents of the token, and move, to…
Bathtub failure rate (BFR) and roller-coaster failure rate (RCFR - a sequence of BFR and inverted BFR (IBFR)) shapes are among the non-monotone failure rate function (FRF) behaviors often observed in complex or competing risks (CR)…
Statistical inference on graphs is a burgeoning field in the applied and theoretical statistics communities, as well as throughout the wider world of science, engineering, business, etc. In many applications, we are faced with the reality…