Sticky Seeding in Discrete-Time Reversible-Threshold Networks (original) (raw)

Compensatory Seeding in Networks with Varying Avaliability of Nodes

Diffusion of information in social networks takes more and more attention from marketers. New methods and algorithms are constantly developed towards maximizing reach of the campaigns and increasing their effectiveness. One of the important research directions in this area is related to selecting initial nodes of the campaign to result with maximizing its effects represented as total number of infections. To achieve this goal, several strategies were developed and they are based on different network measures and other characteristics of users. The prob-lem is that most of these strategies base on static network proper-ties while typical online networks change over time and are sensi-tive to varying activity of users. In this work a novel strategy is proposed which is based on multiple measures with additional parameters related to nodes availability in time periods prior to the campaign. Presented results show that it is possible to com-pensate users with high network measures by others having high frequency of system usage, which, instead, may be easier or cheaper to acquire.

Diffusion of behavior in network games with threshold dynamics

Mathematical Social Sciences, 2016

Research Highlights: • The main novelty of the paper is to assume that the thresholds are endogenously determined. Agents change their inclination by exposition to other inclinations in the social network. • With our model we are able to explain a variety of adoption behavior. Of particular interest is the existence of non-monotonic behavior of the aggregate adoption rate which is not possible in the benchmark model without inclination. Our model is therefore able to explain "sudden" outbreaks of collective action. • This suggests to reinvent the common static and exogenous concept of a tipping point by defining it endogenously generated by the network.

Threshold-limited spreading in social networks with multiple initiators

Scientific Reports, 2013

A classical model for social-influence-driven opinion change is the threshold model. Here we study cascades of opinion change driven by threshold model dynamics in the case where multiple initiators trigger the cascade, and where all nodes possess the same adoption threshold w. Specifically, using empirical and stylized models of social networks, we study cascade size as a function of the initiator fraction p. We find that even for arbitrarily high value of w, there exists a critical initiator fraction p c (w) beyond which the cascade becomes global. Network structure, in particular clustering, plays a significant role in this scenario. Similarly to the case of single-node or single-clique initiators studied previously, we observe that community structure within the network facilitates opinion spread to a larger extent than a homogeneous random network. Finally, we study the efficacy of different initiator selection strategies on the size of the cascade and the cascade window.

Spread of influence in weighted networks under time and budget constraints

Theoretical Computer Science, 2015

Given a network represented by a weighted directed graph G, we consider the problem of finding a bounded cost set of nodes S such that the influence spreading from S in G, within a given time bound, is as large as possible. The dynamic that governs the spread of influence is the following: initially only elements in S are influenced; subsequently at each round, the set of influenced elements is augmented by all nodes in the network that have a sufficiently large number of already influenced neighbors. We prove that the problem is NP-hard, even in simple networks like complete graphs and trees. We also derive a series of positive results. We present exact pseudo-polynomial time algorithms for general trees, that become polynomial time in case the trees are unweighted. This last result improves on previously published results. We also design polynomial time algorithms for general weighted paths and cycles, and for unweighted complete graphs.

Computational aspects of optimal strategic network diffusion

Theoretical Computer Science

Diffusion on complex networks is often modeled as a stochastic process. Yet, recent work on strategic diffusion emphasizes the decision power of agents [1] and treats diffusion as a strategic problem. Here we study the computational aspects of strategic diffusion, i.e., finding the optimal sequence of nodes to activate a network in the minimum time. We prove that finding an optimal solution to this problem is NP-complete in a general case. To overcome this computational difficulty, we present an algorithm to compute an optimal solution based on a dynamic programming technique. We also show that the problem is fixed parameter-tractable when parametrized by the product of the treewidth and maximum degree. We analyze the possibility of developing an efficient approximation algorithm and show that two heuristic algorithms proposed so far cannot have better than a logarithmic approximation guarantee. Finally, we prove that the problem does not admit better than a logarithmic approximation, unless P=NP.

Influence Maximization Through Scheduled Seeding in a Real-World Setting

IEEE Transactions on Computational Social Systems, 2022

In this article, we evaluate, for the first time, the potential of a scheduled seeding strategy for influence maximization in a real-world setting. We first propose methods for analyzing historical data to quantify the infection probability of a node with a given set of properties in a given time and assess the potential of a given seeding strategy to infect nodes. Then, we examine the potential of a scheduled seeding strategy by analyzing a real-world large-scale dataset containing both the network topology as well as the nodes’ infection times. Specifically, we use the proposed methods to demonstrate the existence of two important effects in our dataset: a complex contagion effect and a diminishing social influence effect. As shown in a recent study, the scheduled seeding approach is expected to benefit greatly from the existence of these two effects. Finally, we compare a number of benchmark seeding strategies to a scheduled seeding strategy that ranks nodes based on a combination of the number of infectious friends (NIF) they have, as well as the time that has passed since they became infectious. Results of our analyses show that for a seeding budget of 1%, the scheduled seeding strategy yields a convergence rate that is 14% better than a seeding strategy based solely on their degrees, and 215% better than a random seeding strategy, which is often used in practice.

Time-Bounded Influence Diffusion with Incentives

2018

A widely studied model of influence diffusion in social networks represents the network as a graph \(G=(V,E)\) with an influence threshold t(v) for each node. Initially the members of an initial set \(S\subseteq V\) are influenced. During each subsequent round, the set of influenced nodes is augmented by including every node v that has at least t(v) previously influenced neighbours. The general problem is to find a small initial set that influences the whole network. In this paper we extend this model by using incentives to reduce the thresholds of some nodes. The goal is to minimize the total of the incentives required to ensure that the process completes within a given number of rounds. The problem is hard to approximate in general networks. We present polynomial-time algorithms for paths, trees, and complete networks.

Better Bounds on the Adaptivity Gap of Influence Maximization under Full-adoption Feedback

Proceedings of the AAAI Conference on Artificial Intelligence, 2021

In the influence maximization (IM) problem, we are given a social network and a budget , and we look for a set of nodes in the network, called seeds, that maximize the expected number of nodes that are reached by an influence cascade generated by the seeds, according to some stochastic model for influence diffusion. Extensive studies have been done on the IM problem, since his definition by Kempe, Kleinberg, and Tardos (2003). However, most of the work focuses on the nonadaptive version of the problem where all the seed nodes must be selected before that the cascade starts. In this paper we study the adaptive IM, where the nodes are selected sequentially one by one, and the decision on the th seed can be based on the observed cascade produced by the first − 1 seeds. We focus on the full-adoption feedback in which we can observe the entire cascade of each previously selected seed and on the independent cascade model where each edge is associated with an independent probability of diffusing influence. Previous works showed that there are constant upper bounds on the adaptivity gap, which compares the performance of an adaptive algorithm against a non-adaptive one, but the analyses used to prove these bounds only works for specific graph classes such as in-arborescences, out-arborescences, and one-directional bipartite graphs. Our main result is the first sub-linear upper bound that holds for any graph. Specifically, we show that the adaptivity gap is upper-bounded by 1/3 , where is the number of nodes in the graph. Moreover we improve over the known upper bound for in-arborescences from 2 −1 ≈ 3.16 to 2 2 2 −1 ≈ 2.31. Finally, we study-bounded graphs, a class of undirected graphs in which the sum of node degrees higher than two is at most , and show that the adaptivity gap is upper-bounded by √ + (1). Moreover, we show that in 0-bounded graphs, i.e. undirected graphs in which each connected component is a path or a cycle, the adaptivity gap is at most 3 3 3 −1 ≈ 3.16. To prove our bounds, we introduce new techniques to relate adaptive policies with non-adaptive ones that might be of their own interest.

Influence maximization under limited network information: Seeding high-degree neighbors

arXiv (Cornell University), 2022

The diffusion of information, norms, and practices across a social network can be initiated by compelling a small number of seed individuals to adopt first. Strategies proposed in previous work either assume full network information or large degree of control over what information is collected. However, privacy settings on the Internet and high non-response in surveys often severely limit available connectivity information.Here we propose a seeding strategy for scenarios with limited network information: Only the degrees and connections of some random nodes are known. This new strategy is a modification of "random neighbor sampling" and seeds the highest-degree neighbors of randomly selected nodes. In simulations of a linear threshold model on a range of synthetic and real-world networks, we find that this new strategy outperforms other seeding strategies, including high-degree seeding and clustered seeding.