Explaining Snapshots of Network Diffusions: Structural and Hardness Results

Much research has been done on studying the diffusion of ideas or technologies on social networks including the \textit{Influence Maximization} problem and many of its variations. Here, we investigate a type of inverse problem. Given a snapshot of the diffusion process, we seek to understand if the snapshot is feasible for a given dynamic, i.e., whether there is a limited number of nodes whose initial adoption can result in the snapshot in finite time. While similar questions have been considered for epidemic dynamics, here, we consider this problem for variations of the deterministic Linear Threshold Model, which is more appropriate for modeling strategic agents. Specifically, we consider both sequential and simultaneous dynamics when deactivations are allowed and when they are not. Even though we show hardness results for all variations we consider, we show that the case of sequential dynamics with deactivations allowed is significantly harder than all others. In contrast, sequential dynamics make the problem trivial on cliques even though it's complexity for simultaneous dynamics is unknown. We complement our hardness results with structural insights that can help better understand diffusions of social networks under various dynamics.Comment: 14 pages, 3 figure

Minimizing Seed Set Selection with Probabilistic Coverage Guarantee in a Social Network

A topic propagating in a social network reaches its tipping point if the number of users discussing it in the network exceeds a critical threshold such that a wide cascade on the topic is likely to occur. In this paper, we consider the task of selecting initial seed users of a topic with minimum size so that with a guaranteed probability the number of users discussing the topic would reach a given threshold. We formulate the task as an optimization problem called seed minimization with probabilistic coverage guarantee (SM-PCG). This problem departs from the previous studies on social influence maximization or seed minimization because it considers influence coverage with probabilistic guarantees instead of guarantees on expected influence coverage. We show that the problem is not submodular, and thus is harder than previously studied problems based on submodular function optimization. We provide an approximation algorithm and show that it approximates the optimal solution with both a multiplicative ratio and an additive error. The multiplicative ratio is tight while the additive error would be small if influence coverage distributions of certain seed sets are well concentrated. For one-way bipartite graphs we analytically prove the concentration condition and obtain an approximation algorithm with an $O(\log n)$ multiplicative ratio and an $O(\sqrt{n})$ additive error, where $n$ is the total number of nodes in the social graph. Moreover, we empirically verify the concentration condition in real-world networks and experimentally demonstrate the effectiveness of our proposed algorithm comparing to commonly adopted benchmark algorithms.Comment: Conference version will appear in KDD 201

Technology diffusion in communication networks

The deployment of new technologies in the Internet is notoriously difficult, as evidence by the myriad of well-developed networking technologies that still have not seen widespread adoption (e.g., secure routing, IPv6, etc.) A key hurdle is the fact that the Internet lacks a centralized authority that can mandate the deployment of a new technology. Instead, the Internet consists of thousands of nodes, each controlled by an autonomous, profit-seeking firm, that will deploy a new networking technology only if it obtains sufficient local utility by doing so. For the technologies we study here, local utility depends on the set of nodes that can be reached by traversing paths consisting only of nodes that have already deployed the new technology. To understand technology diffusion in the Internet, we propose a new model inspired by work on the spread of influence in social networks. Unlike traditional models, where a node's utility depends only its immediate neighbors, in our model, a node can be influenced by the actions of remote nodes. Specifically, we assume node v activates (i.e. deploys the new technology) when it is adjacent to a sufficiently large connected component in the subgraph induced by the set of active nodes; namely, of size exceeding node v's threshold value \theta(v). We are interested in the problem of choosing the right seedset of nodes to activate initially, so that the rest of the nodes in the network have sufficient local utility to follow suit. We take the graph and thresholds values as input to our problem. We show that our problem is both NP-hard and does not admit an (1-o(1) ln|V| approximation on general graphs. Then, we restrict our study to technology diffusion problems where (a) maximum distance between any pair of nodes in the graph is r, and (b) there are at most \ell possible threshold values. Our set of restrictions is quite natural, given that (a) the Internet graph has constant diameter, and (b) the fact that limiting the granularity of the threshold values makes sense given the difficulty in obtaining empirical data that parameterizes deployment costs and benefits. We present algorithm that obtains a solution with guaranteed approximation rate of O(r^2 \ell \log|V|) which is asymptotically optimal, given our hardness results. Our approximation algorithm is a linear-programming relaxation of an 0-1 integer program along with a novel randomized rounding scheme.National Science Foundation (S-1017907, CCF-0915922

Propagation d’événements dans un graphe économique

International audienceThe diffusion models of infections in social networks are intensively studied these last years. The existing studies concern in particular disease and rumor diffusions in social networks or financial risk in banking networks. We propose in this paper to study the diffusion problem of events within social and economic networks. In particular, we define a new problem of diffusion called the Influence Classification Problem. The objective is to find the set of nodes which are impacted by a given network. We also propose two diffusion models based on a computed threshold according to the graph and event attributes. We test our models ontwo real and known events : the hurricane Katrina and the fusion of Bayer and MonsantoLes modèles de diffusion dans les réseaux sociaux sont beaucoup étudiés ces dernières années. Les études concernent notamment les diffusions de maladies et de rumeurs dans les réseaux sociaux ou de risques financiers dans les réseaux bancaires. Nous proposons dans cet article de répondre au problème de diffusion des événements au sein de réseaux économico-sociaux. En particulier, nous proposons d’étudier un nouveau problème de diffusion appelé Influence Classification Problem (ICP) dont l’objectif est de classifier automatiquement quels noeuds sont impactés pour un événement donné. Nous proposons également deux modèles de propagation basés sur un seuil calculé en fonction desattributs du graphe et de l’événement. Nous testons nos modèles sur deux événements connus : l’ouragan Katrina et l’acquisition de Monsanto par Bayer

ALGORITHMS FOR MASSIVE, EXPENSIVE, OR OTHERWISE INCONVENIENT GRAPHS

A long-standing assumption common in algorithm design is that any part of the input is accessible at any time for unit cost. However, as we work with increasingly large data sets, or as we build smaller devices, we must revisit this assumption. In this thesis, I present some of my work on graph algorithms designed for circumstances where traditional assumptions about inputs do not apply. 1. Classical graph algorithms require direct access to the input graph and this is not feasible when the graph is too large to fit in memory. For computation on massive graphs we consider the dynamic streaming graph model. Given an input graph defined by as a stream of edge insertions and deletions, our goal is to approximate properties of this graph using space that is sublinear in the size of the stream. In this thesis, I present algorithms for approximating vertex connectivity, hypergraph edge connectivity, maximum coverage, unique coverage, and temporal connectivity in graph streams. 2. In certain applications the input graph is not explicitly represented, but its edges may be discovered via queries which require costly computation or measurement. I present two open-source systems which solve real-world problems via graph algorithms which may access their inputs only through costly edge queries. M ESH is a memory manager which compacts memory efficiently by finding an approximate graph matching subject to stringent time and edge query restrictions. PathCache is an efficiently scalable network measurement platform that outperforms the current state of the art

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum

Railroads, Their Regulation, and Its Effect on Efficiency and Competition

Railroads have been subject to federal regulation since 1887. Due to the development of competing modes of transportation and changes in types of products being shipped, regulation began to impede efficiency and viability of firms, leading to partial deregulation of the industry in 1980. Partial deregulation allowed railroads to reduce costs, notably through mergers and line abandonment, which were aggressively pursued following deregulation and led to dramatic efficiency gains. However, concerns remain over increased consolidation, lack of competition in the industry, and the ability of firms to continue to realize efficiency gains. This dissertation investigates more recent developments in the rail industry with an eye towards regulation's effect and role. I begin with a study into the markups of price over marginal cost and elasticities of scale in the rail industry. Scale elasticities provide information on where firms are operating on their average cost curves, and markups provide a more theoretically appealing method of examining pricing behavior than the revenue-to-variable-cost measure currently used by regulators. I extend previously developed methods to identify markups and scales for each firm and in each year. I find prices well in excess of marginal cost, and evidence firms are operating near minimum efficient scale, indicating efficiency gains from deregulation may be fully realized. I then present a study that examines productivity changes in the rail industry and the role of technological change. I extend stochastic frontier frameworks to allow productivity and the state of technology to evolve flexibly through time and vary across firms. I find firms turn towards technological innovation to realize productivity gains when other channels previously offered by deregulation are not available. I finish with a study of allocative errors in the rail industry. I again extend a stochastic frontier model to include differences in production across firms and allow allocative errors to be correlated with competitive pressures. I find that incorporating flexibility into the description of firm production is crucial for obtaining unbiased estimates of allocative errors, overcapitalization is prevalent in the rate-regulated rail industry, and additional competition does not appear to reduce inefficiency. This dissertation includes unpublished co-authored material

Information design in service systems and online markets

In mechanism design, the firm has an advantage over its customers in its knowledge of the state of the system, which can affect the utilities of all players. This poses the question: how can the firm utilize that information (and not additional financial incentives) to persuade customers to take actions that lead to higher revenue (or other firm utility)? When the firm is constrained to ``cheap talk,'' and cannot credibly commit to a manner of signaling, the firm cannot change customer behavior in a meaningful way. Instead, we allow firm to commit to how they will signal in advance. Customers can then trust the signals they receive and act on their realization. This thesis contains the work of three papers, each of which applies information design to service systems and online markets. We begin by examining how a firm could signal a queue's length to arriving, impatient customers in a service system. We show that the choice of an optimal signaling mechanism can be written as a infinite linear program and then show an intuitive form for its optimal solution. We show that with the optimal fixed price and optimal signaling, a firm can generate the same revenue as it could with an observable queue and length-dependent variable prices. Next, we study demand and inventory signaling in online markets: customers make strategic purchasing decisions, knowing the price will decrease if an item does not sell out. The firm aims to convince customers to buy now at a higher price. We show that the optimal signaling mechanism is public, and sends all customers the same information. Finally, we consider customers whose ex ante utility is not simply their expected ex post utility, but instead a function of its distribution. We bound the number of signals needed for the firm to generate their optimal utility and provide a convex program reduction of the firm's problem

Resource Efficient Large-Scale Machine Learning

Non-parametric models provide a principled way to learn non-linear functions. In particular, kernel methods are accurate prediction tools that rely on solid theoretical foundations. Although they enjoy optimal statistical properties, they have limited applicability in real-world large-scale scenarios because of their stringent computational requirements in terms of time and memory. Indeed their computational costs scale at least quadratically with the number of points of the dataset and many of the modern machine learning challenges requires training on datasets of millions if not billions of points. In this thesis, we focus on scaling kernel methods, developing novel algorithmic solutions that incorporate budgeted computations. To derive these algorithms we mix ideas from statistics, optimization, and randomized linear algebra. We study the statistical and computational trade-offs for various non-parametric models, the key component to derive numerical solutions with resources tailored to the statistical accuracy allowed by the data. In particular, we study the estimator defined by stochastic gradients and random features, showing how all the free parameters provably govern both the statistical properties and the computational complexity of the algorithm. We then see how to blend the Nystr\uf6m approximation and preconditioned conjugate gradient to derive a provably statistically optimal solver that can easily scale on datasets of millions of points on a single machine. We also derive a provably accurate leverage score sampling algorithm that can further improve the latter solver. Finally, we see how the Nystr\uf6m approximation with leverage scores can be used to scale Gaussian processes in a bandit optimization setting deriving a provably accurate algorithm. The theoretical analysis and the new algorithms presented in this work represent a step towards building a new generation of efficient non-parametric algorithms with minimal time and memory footprints