arXiv subjects

Mansi Sood

Publications and source records attributed to Mansi Sood.

10 recordsLinked to original sources

arXiv2025

On Balancing Sparsity with Reliable Connectivity in Distributed Network Design with Random K-out Graphs

In several applications in distributed systems, an important design criterion is ensuring that the network is sparse, i.e., does not contain too many edges, while achieving reliable connectivity. Sparsity ensures communication overhead remains low, while reliable connectivity is tied to reliable communication and inference on decentralized data reservoirs and computational resources. A class of network models called random K-out graphs appear widely as a heuristic to balance connectivity and sparsity, especially in settings with limited trust, e.g., privacy-preserving aggregation of networked data in which networks are deployed. However, several questions remain regarding how to choose network parameters in response to different operational requirements, including the need to go beyond asymptotic results and the ability to model the stochastic and adversarial environments. To address this gap, we present theorems to inform the choice of network parameters that guarantee reliable connectivity in regimes where nodes can be finite or unreliable. We first derive upper and lower bounds for probability of connectivity in random K-out graphs when the number of nodes is finite. Next, we analyze the property of r-robustness, a stronger notion than connectivity that enables resilient consensus in the presence of malicious nodes. Finally, motivated by aggregation mechanisms based on pairwise masking, we model and analyze the impact of a subset of adversarial nodes, modeled as deletions, on connectivity and giant component size - metrics that are closely tied to privacy guarantees. Together, our results pave the way for end-to-end performance guarantees for a suite of algorithms for reliable inference on networks.

cs.SI↗

arXiv2024

On the Interplay of Clustering and Evolution in the Emergence of Epidemic Outbreaks

In an increasingly interconnected world, a key scientific challenge is to examine mechanisms that lead to the widespread propagation of contagions, such as misinformation and pathogens, and identify risk factors that can trigger large-scale outbreaks. Underlying both the spread of disease and misinformation epidemics is the evolution of the contagion as it propagates, leading to the emergence of different strains, e.g., through genetic mutations in pathogens and alterations in the information content. Recent studies have revealed that models that do not account for heterogeneity in transmission risks associated with different strains of the circulating contagion can lead to inaccurate predictions. However, existing results on multi-strain spreading assume that the network has a vanishingly small clustering coefficient, whereas clustering is widely known to be a fundamental property of real-world social networks. In this work, we investigate spreading processes that entail evolutionary adaptations on random graphs with tunable clustering and arbitrary degree distributions. We derive a mathematical framework to quantify the epidemic characteristics of a contagion that evolves as it spreads, with the structure of the underlying network as given via arbitrary {\em joint} degree distributions of single-edges and triangles. To the best of our knowledge, our work is the first to jointly analyze the impact of clustering and evolution on the emergence of epidemic outbreaks. We supplement our theoretical finding with numerical simulations and case studies, shedding light on the impact of clustering on contagion spread.

cs.SI↗

arXiv2023

On the Robustness, Connectivity and Giant Component Size of Random K-out Graphs

Random K-out graphs are garnering interest in designing distributed systems including secure sensor networks, anonymous crypto-currency networks, and differentially-private decentralized learning. In these security-critical applications, it is important to model and analyze the resilience of the network to node failures and adversarial captures. Motivated by this, we analyze how the connectivity properties of random K-out graphs vary with the network parameters $K$, the number of nodes ($n$), and the number of nodes that get failed or compromised ($γ_n$). In particular, we study the conditions for achieving \emph{connectivity} {with high probability} and for the existence of a \emph{giant component} with formal guarantees on the size of the largest connected component in terms of the parameters $n,~K$, and $γ_n$. Next, we analyze the property of \emph{$r$-robustness} which is a stronger property than connectivity and leads to resilient consensus in the presence of malicious nodes. We derive conditions on $K$ and $n$ under which the random K-out graph achieves r-robustness with high probability. We also provide extensive numerical simulations and compare our results on random K-out graphs with known results on Erdős-Rényi (ER) graphs.

cs.IT↗

arXiv2023

Spreading Processes with Mutations over Multi-layer Networks

A key scientific challenge during the outbreak of novel infectious diseases is to predict how the course of the epidemic changes under different countermeasures that limit interaction in the population. Most epidemiological models do not consider the role of mutations and heterogeneity in the type of contact events. However, pathogens have the capacity to mutate in response to changing environments, especially caused by the increase in population immunity to existing strains and the emergence of new pathogen strains poses a continued threat to public health. Further, in light of differing transmission risks in different congregate settings (e.g., schools and offices), different mitigation strategies may need to be adopted to control the spread of infection. We analyze a multi-layer multi-strain model by simultaneously accounting for i) pathways for mutations in the pathogen leading to the emergence of new pathogen strains, and ii) differing transmission risks in different congregate settings, modeled as network-layers. Assuming complete cross-immunity among strains, namely, recovery from any infection prevents infection with any other (an assumption that will need to be relaxed to deal with COVID-19 or influenza), we derive the key epidemiological parameters for the proposed multi-layer multi-strain framework. We demonstrate that reductions to existing network-based models that discount heterogeneity in either the strain or the network layers can lead to incorrect predictions for the course of the outbreak. In addition, our results highlight that the impact of imposing/lifting mitigation measures concerning different contact network layers (e.g., school closures or work-from-home policies) should be evaluated in connection with their effect on the likelihood of the emergence of new pathogen strains.

physics.soc-ph↗

arXiv2021

Existence and Size of the Giant Component in Inhomogeneous Random K-out Graphs

Random K-out graphs are receiving attention as a model to construct sparse yet well-connected topologies in distributed systems including sensor networks, federated learning, and cryptocurrency networks. In response to the growing heterogeneity in emerging real-world networks, where nodes differ in resources and requirements, inhomogeneous random K-out graphs, denoted by $H(n;μ,K_n)$, were proposed recently. Motivated by practical settings where establishing links is costly and only a bounded choice of $K_n$ is feasible ($K_n = O(1)$), we study the size of the largest connected sub-network of $H(n;μ,K_n)$, We first show that the trivial condition of $K_n \geq 2$ for all $n$ is sufficient to ensure that $H(n;μ,K_n)$, contains a giant component of size $n-O(1)$ whp. Next, to model settings where nodes can fail or get compromised, we investigate the size of the largest connected sub-network in $H(n;μ,K_n)$, when $d_n$ nodes are selected uniformly at random and removed from the network. We show that if $d_n=O(1)$, a giant component of size $n- \OO(1)$ persists for all $K_n \geq 2$ whp. Further, when $d_n=o(n)$ nodes are removed from $H(n;μ,K_n)$, the remaining nodes contain a giant component of size $n(1-o(1))$ whp for all $K_n \geq 2$. We present numerical results to demonstrate the size of the largest connected component when the number of nodes is finite.

cs.IT↗

arXiv2021

On the Connectivity and Giant Component Size of Random K-out Graphs Under Randomly Deleted Nodes

Random K-out graphs, denoted $\mathbb{H}(n;K)$, are generated by each of the $n$ nodes drawing $K$ out-edges towards $K$ distinct nodes selected uniformly at random, and then ignoring the orientation of the arcs. Recently, random K-out graphs have been used in applications as diverse as random (pairwise) key predistribution in ad-hoc networks, anonymous message routing in crypto-currency networks, and differentially-private federated averaging. In many applications, connectivity of the random K-out graph when some of its nodes are dishonest, have failed, or have been captured is of practical interest. We provide a comprehensive set of results on the connectivity and giant component size of $\mathbb{H}(n;K_n,γ_n)$, i.e., random K-out graph when $γ_n$ of its nodes, selected uniformly at random, are deleted. First, we derive conditions for $K_n$ and $n$ that ensure, with high probability (whp), the connectivity of the remaining graph when the number of deleted nodes is $γ_n=Ω(n)$ and $γ_n=o(n)$, respectively. Next, we derive conditions for $\mathbb{H}(n;K_n,γ_n)$ to have a giant component, i.e., a connected subgraph with $Ω(n)$ nodes, whp. This is also done for different scalings of $γ_n$ and upper bounds are provided for the number of nodes outside the giant component. Simulation results are presented to validate the usefulness of the results in the finite node regime.

cs.IT↗

arXiv2020

Tight Bounds for Connectivity of Random K-out Graphs

Random K-out graphs are used in several applications including modeling by sensor networks secured by the random pairwise key predistribution scheme, and payment channel networks. The random K-out graph with $n$ nodes is constructed as follows. Each node draws an edge towards $K$ distinct nodes selected uniformly at random. The orientation of the edges is then ignored, yielding an undirected graph. An interesting property of random K-out graphs is that they are connected almost surely in the limit of large $n$ for any $K \geq2$. This means that they attain the property of being connected very easily, i.e., with far fewer edges ($O(n)$) as compared to classical random graph models including Erdős-Rényi graphs ($O(n \log n)$). This work aims to reveal to what extent the asymptotic behavior of random K-out graphs being connected easily extends to cases where the number $n$ of nodes is small. We establish upper and lower bounds on the probability of connectivity when $n$ is finite. Our lower bounds improve significantly upon the existing results, and indicate that random K-out graphs can attain a given probability of connectivity at much smaller network sizes than previously known. We also show that the established upper and lower bounds match order-wise; i.e., further improvement on the order of $n$ in the lower bound is not possible. In particular, we prove that the probability of connectivity is $1-Θ({1}/{n^{K^2-1}})$ for all $K \geq 2$. Through numerical simulations, we show that our bounds closely mirror the empirically observed probability of connectivity.

cs.IT↗

arXiv2020

On the Strength of Connectivity of Inhomogeneous Random K-out Graphs

Random graphs are an important tool for modelling and analyzing the underlying properties of complex real-world networks. In this paper, we study a class of random graphs known as the inhomogeneous random K-out graphs which were recently introduced to analyze heterogeneous sensor networks secured by the pairwise scheme. In this model, first, each of the $n$ nodes is classified as type-1 (respectively, type-2) with probability $0<μ<1$ (respectively, $1-μ)$ independently from each other. Next, each type-1 (respectively, type-2) node draws 1 arc towards a node (respectively, $K_n$ arcs towards $K_n$ distinct nodes) selected uniformly at random, and then the orientation of the arcs is ignored. From the literature on homogeneous K-out graphs wherein all nodes select $K_n$ neighbors (i.e., $μ=0$), it is known that when $K_n \geq2$, the graph is $K_n$-connected asymptotically almost surely (a.a.s.) as $n$ gets large. In the inhomogeneous case (i.e., $μ>0$), it was recently established that achieving even 1-connectivity a.a.s. requires $K_n=ω(1)$. Here, we provide a comprehensive set of results to complement these existing results. First, we establish a sharp zero-one law for $k$-connectivity, showing that for the network to be $k$-connected a.a.s., we need to set $K_n = \frac{1}{1-μ}(\log n +(k-2)\log\log n + ω(1))$ for all $k=2, 3, \ldots$. Despite such large scaling of $K_n$ being required for $k$-connectivity, we show that the trivial condition of $K_n \geq 2$ for all $n$ is sufficient to ensure that inhomogeneous K-out graph has a connected component of size $n-O(1)$ whp.

cs.IT↗

arXiv2020

Duopolistic platform competition for revenue and throughput

We consider two competing platforms operating in a two-sided market and offering identical services to their customers at potentially different prices. The objective of each platform is to maximize its throughput or revenue by suitably pricing its services. We assume that customers have a preference or loyalty to the platforms while the workers freelance for the two platforms. Assuming that the resulting interaction between the users is such that their aggregate utility is maximized, we show that for each value of the loyalty, there exists a pure strategy Nash equilibrium for both the throughput and revenue competition game and characterize it.

math.OC↗

arXiv2019

Towards $k$-connectivity in Heterogeneous Sensor Networks under Pairwise Key Predistribution

We study the secure and reliable connectivity of wireless sensor networks under the heterogeneous pairwise key predistribution scheme. This scheme was recently introduced as an extension of the random pairwise key predistribution scheme of Chan et al. to accommodate networks where the constituent sensors have different capabilities or requirements for security and connectivity. For simplicity, we consider a heterogeneous network where each of the $n$ sensors is classified as type-1 (respectively, type-2) with probability $μ$ (respectively, $1-μ)$ where $0<μ<1$. Each type-1 (respectively, type-2) node selects 1 (respectively, $K_n$) other nodes uniformly at random to be paired with; according to the pairwise scheme each pair is then assigned a unique pairwise key so that they can securely communicate with each other. We establish critical conditions on $n, μ$, and $K_n$ such that the resulting network has minimum node degree of at least $k$ with high probability in the limit of large network size. Our result constitutes a zero-one law for the minimum node degree of the recently introduced inhomogeneous random K-out graph model. This constitutes a crucial step towards establishing a similar zero-one law for the $k$-connectivity of the graph; i.e., for the property that the network remains connected despite the failure of any $k-1$ nodes or links. We present numerical results that indicate the usefulness of our results in selecting the parameters of the scheme in practical settings with finite number of sensors.

cs.IT↗