Models for the processes by which ideas and influence propagate through a social network have been studied in a number of domains, including the diffusion of medical and technological innovations, the sudden and widespread adoption of various strategies in game-theoretic settings, and the effects of “word of mouth ” in the promotion of new products. Recently, motivated by the design of viral marketing strategies, Domingos and Richardson posed a fundamental algorithmic problem for such social network processes: if we can try to convince a subset of individuals to adopt a new product or innovation, and the goal is to trigger a large cascade of further adoptions, which set of individuals should we target? We consider this problem in several of the most widely studied models in social network analysis. The optimization problem of selecting the most influential nodes is NP-hard here, and we provide the first provable approximation guarantees for efficient algorithms. Using an analysis framework based on submodular functions, we show that a natural greedy strategy obtains a solution that is provably within 63 % of optimal for several classes of models; our framework suggests a general approach for reasoning about the performance guarantees of algorithms for these types of influence problems in social networks. We also provide computational experiments on large collaboration networks, showing that in addition to their provable guarantees, our approximation algorithms significantly out-perform nodeselection heuristics based on the well-studied notions of degree centrality and distance centrality from the field of social networks.

This paper presents 7DS, a novel peer-to-peer data sharing system. 7DS is an architecture, a set of protocols and an implementation enabling the exchange of data among peers that are not necessarily connected to the Internet. Peers can be either mobile or stationary. It anticipates the information needs of users and fulfills them by searching for information among peers. We evaluate via extensive simulations the effectiveness of our system for data dissemination among mobile devices with a large number of user mobility scenarios. We model several general data dissemination approaches and investigate the effect of the wireless coverage range, 7DS host density, query interval and cooperation strategy among the mobile hosts. Using theory from random walks, random environments and diffusion of controlled processes, we model one of these data dissemination schemes and show that the analysis confirms the simulation results for this scheme. 1.

Abstract—We present an architecture that enables the sharing of information among mobile, wireless, collaborating hosts that are intermittently connected to the Internet. Participants in the system obtain data objects from Internet-connected servers, cache them and exchange them with others who are interested in them. The system exploits the fact that there is a high locality of information access within a geographic area. It aims to increase the data availability to participants with lost connectivity to the Internet. We investigate how user mobility and query patterns affect data dissemination in such an environment. We discuss the main components of the system and possible applications. Finally, we present simulation results that show that the ad hoc networks can be very effective in distributing popular information. I.

I continue the study, begun in Blume (1993), of stochastic strategy revision processes in large player populations where the range of interaction between players is small. Each player interacts directly with only a finite set of neighbors, but any two players indirectly interact through a finite chain of direct interactions. The purpose of this paper is to compare local strategic interaction with global strategic interaction when players update their choice according to the (myopic) best-response rule. I show that randomizing the order in which players update their strategic choice is sufficient to achieve coordination on the risk-dominant strategy in symmetric 2 x 2 coordination games. The "persistant randomness" which is necessary to achieve similar coordination when the range of interaction is global is replaced by spatial variation in choice in the initial condition when strategic interactions are local. An extension of the risk-dominance idea gives the same convergence result for K x K games with strategic complementarities. Similar results for K x K pure coordination games and potential games are also presented.

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The flow of information or influence through a large social network can be thought of as unfolding with the dynamics of an epidemic: as individuals become aware of new ideas, tech-nologies, fads, rumors, or gossip, they have the potential to pass them on to their friends and colleagues, causing the resulting behavior to cascade through the network. We consider a collection of probabilistic and game-theoretic models for such phenomena proposed in the mathematical social sciences, as well as recent algorithmic work on the problem by computer scientists. Building on this, we discuss the implications of cascading behavior in a number of on-line settings, including word-of-mouth effects (also known as “viral marketing”) in the success of new products, and the influence of social networks in the growth of on-line communities. 1

We prove and extend a conjecture of Kempe, Kleinberg, and Tardos (KKT) on the spread of influence in social networks. A social network can be represented by a directed graph where the nodes are individuals and the edges indicate a form of social relationship. A simple way to model the diffusion of ideas, innovative behavior, or “word-of-mouth ” effects on such a graph is to consider an increasing process of “infected” (or active) nodes: each node becomes infected once an activation function of the set of its infected neighbors crosses a certain threshold value. Such a model was introduced by KKT in [7, 8] where the authors also impose several natural assumptions: the threshold values are (uniformly) random to account for our lack of knowledge of the true values; and the activation functions are monotone and submodular, i.e. have “diminishing returns. ” The monotonicity condition indicates that a node is more likely to become active if more of its neighbors are active, while the submodularity condition, indicates that the marginal effect of each neighbor is decreasing when the set of active neighbors increases. For an initial set of active nodes S, let σ(S) denote the expected number of active nodes at termination. Here we prove a conjecture of KKT: we show that the function σ(S) is submodular under

In this paper, we consider directed polymers in random environment with discrete space and time. For transverse dimension at least equal to 3, we prove that diffusivity holds for the path in the full weak disorder region, i.e., where the partition function differs from its annealed value only by a non-vanishing factor. Deep inside this region, we also show that the quenched averaged energy has fluctuations of order 1. In complete generality (arbitrary dimension and temperature), we prove monotonicity of the phase diagram in the temperature.

Abstract.Any infinite graph G = (V, E) has a site percolation critical probability psite c and a bond percolation critical probability pbond c. The well known weak inequality psite c ≥ pbond c is strengthened to strict inequality for a broad category of graphs G, including all the usual finite-dimensional lattices in two and more dimensions. The complementary inequality psite c ≤ 1 − (1 − pbond c) ∆−1 is proved also, where ∆ denotes the supremum of the vertex degrees of G. 0. Introduction and results Let G = (V, E) be an infinite connected graph. Our target in this paper is study the relationship between site and bond percolation on G, and particularly to prove inequalities between the two critical probabilities psite c, pbond c of these models. To

In this paper we will investigate dynamic stability of percolation for the stochastic Ising model and the contact process. We also introduce the notion of downward and upward ε-movability which will be a key tool for our analysis. 1. Introduction. Consider