Exact Computation of Influence Spread by Binary Decision Diagrams

Evaluating influence spread in social networks is a fundamental procedure to estimate the word-of-mouth effect in viral marketing. There are enormous studies about this topic; however, under the standard stochastic cascade models, the exact computation of influence spread is known to be #P-hard. Thus, the existing studies have used Monte-Carlo simulation-based approximations to avoid exact computation. We propose the first algorithm to compute influence spread exactly under the independent cascade model. The algorithm first constructs binary decision diagrams (BDDs) for all possible realizations of influence spread, then computes influence spread by dynamic programming on the constructed BDDs. To construct the BDDs efficiently, we designed a new frontier-based search-type procedure. The constructed BDDs can also be used to solve other influence-spread related problems, such as random sampling without rejection, conditional influence spread evaluation, dynamic probability update, and gradient computation for probability optimization problems. We conducted computational experiments to evaluate the proposed algorithm. The algorithm successfully computed influence spread on real-world networks with a hundred edges in a reasonable time, which is quite impossible by the naive algorithm. We also conducted an experiment to evaluate the accuracy of the Monte-Carlo simulation-based approximation by comparing exact influence spread obtained by the proposed algorithm.Comment: WWW'1

Seeding with Costly Network Information

We study the task of selecting $k$ nodes in a social network of size $n$, to seed a diffusion with maximum expected spread size, under the independent cascade model with cascade probability $p$. Most of the previous work on this problem (known as influence maximization) focuses on efficient algorithms to approximate the optimal seed set with provable guarantees, given the knowledge of the entire network. However, in practice, obtaining full knowledge of the network is very costly. To address this gap, we first study the achievable guarantees using $o(n)$ influence samples. We provide an approximation algorithm with a tight (1-1/e){\mbox{OPT}}-\epsilon n guarantee, using $O_{\epsilon}(k^2\log n)$ influence samples and show that this dependence on $k$ is asymptotically optimal. We then propose a probing algorithm that queries ${O}_{\epsilon}(p n^2\log^4 n + \sqrt{k p} n^{1.5}\log^{5.5} n + k n\log^{3.5}{n})$ edges from the graph and use them to find a seed set with the same almost tight approximation guarantee. We also provide a matching (up to logarithmic factors) lower-bound on the required number of edges. To address the dependence of our probing algorithm on the independent cascade probability $p$, we show that it is impossible to maintain the same approximation guarantees by controlling the discrepancy between the probing and seeding cascade probabilities. Instead, we propose to down-sample the probed edges to match the seeding cascade probability, provided that it does not exceed that of probing. Finally, we test our algorithms on real world data to quantify the trade-off between the cost of obtaining more refined network information and the benefit of the added information for guiding improved seeding strategies

Capacity Constrained Influence Maximization in Social Networks

Influence maximization (IM) aims to identify a small number of influential individuals to maximize the information spread and finds applications in various fields. It was first introduced in the context of viral marketing, where a company pays a few influencers to promote the product. However, apart from the cost factor, the capacity of individuals to consume content poses challenges for implementing IM in real-world scenarios. For example, players on online gaming platforms can only interact with a limited number of friends. In addition, we observe that in these scenarios, (i) the initial adopters of promotion are likely to be the friends of influencers rather than the influencers themselves, and (ii) existing IM solutions produce sub-par results with high computational demands. Motivated by these observations, we propose a new IM variant called capacity constrained influence maximization (CIM), which aims to select a limited number of influential friends for each initial adopter such that the promotion can reach more users. To solve CIM effectively, we design two greedy algorithms, MG-Greedy and RR-Greedy, ensuring the $1/2$-approximation ratio. To improve the efficiency, we devise the scalable implementation named RR-OPIM+ with $(1/2-\epsilon)$-approximation and near-linear running time. We extensively evaluate the performance of 9 approaches on 6 real-world networks, and our solutions outperform all competitors in terms of result quality and running time. Additionally, we deploy RR-OPIM+ to online game scenarios, which improves the baseline considerably.Comment: The technical report of the paper entitled 'Capacity Constrained Influence Maximization in Social Networks' in SIGKDD'2

Maximizing the Diversity of Exposure in a Social Network

Social-media platforms have created new ways for citizens to stay informed and participate in public debates. However, to enable a healthy environment for information sharing, social deliberation, and opinion formation, citizens need to be exposed to sufficiently diverse viewpoints that challenge their assumptions, instead of being trapped inside filter bubbles. In this paper, we take a step in this direction and propose a novel approach to maximize the diversity of exposure in a social network. We formulate the problem in the context of information propagation, as a task of recommending a small number of news articles to selected users. We propose a realistic setting where we take into account content and user leanings, and the probability of further sharing an article. This setting allows us to capture the balance between maximizing the spread of information and ensuring the exposure of users to diverse viewpoints. The resulting problem can be cast as maximizing a monotone and submodular function subject to a matroid constraint on the allocation of articles to users. It is a challenging generalization of the influence maximization problem. Yet, we are able to devise scalable approximation algorithms by introducing a novel extension to the notion of random reverse-reachable sets. We experimentally demonstrate the efficiency and scalability of our algorithm on several real-world datasets

Composite Community-Aware Diversified Influence Maximization with Efficient Approximation

Influence Maximization (IM) is a famous topic in mobile networks and social computing, which aims at finding a small subset of users to maximize the influence spread through online information cascade. Recently, some careful researchers paid attention to diversity of information dissemination, especially community-aware diversity, and formulated the diversified IM problem. The diversity is ubiquitous in a lot of real-world applications, but they are all based on a given community structure. In social networks, we can form heterogeneous community structures for the same group of users according to different metrics. Therefore, how to quantify the diversity based on multiple community structures is an interesting question. In this paper, we propose the Composite Community-Aware Diversified IM (CC-DIM) problem, which aims at selecting a seed set to maximize the influence spread and the composite diversity over all possible community structures under consideration. To address the NP-hardness of CC-DIM problem, we adopt the technique of reverse influence sampling and design a random Generalized Reverse Reachable (G-RR) set to estimate the objective function. The composition of a random G-RR set is much more complex than the RR set used for the IM problem, which will lead to inefficiency of traditional sampling-based approximation algorithms. Because of this, we further propose a two-stage algorithm, Generalized HIST (G-HIST). It can not only return a $(1-1/e-\varepsilon)$ approximate solution with at least $(1-\delta)$ probability, but also improve the efficiency of sampling and ease the difficulty of searching by significantly reducing the average size of G-RR sets. Finally, we evaluate our G-HIST on real datasets against existing algorithms. The experimental results show the effectiveness of our proposed algorithm and its superiority over other baseline algorithms.Comment: 15 page

Continuous Influence-based Community Partition for Social Networks

Community partition is of great importance in social networks because of the rapid increasing network scale, data and applications. We consider the community partition problem under LT model in social networks, which is a combinatorial optimization problem that divides the social network to disjoint $m$ communities. Our goal is to maximize the sum of influence propagation through maximizing it within each community. As the influence propagation function of community partition problem is supermodular under LT model, we use the method of Lov{$\acute{a}$}sz Extension to relax the target influence function and transfer our goal to maximize the relaxed function over a matroid polytope. Next, we propose a continuous greedy algorithm using the properties of the relaxed function to solve our problem, which needs to be discretized in concrete implementation. Then, random rounding technique is used to convert the fractional solution to integer solution. We present a theoretical analysis with $1-1/e$ approximation ratio for the proposed algorithms. Extensive experiments are conducted to evaluate the performance of the proposed continuous greedy algorithms on real-world online social networks datasets and the results demonstrate that continuous community partition method can improve influence spread and accuracy of the community partition effectively.Comment: arXiv admin note: text overlap with arXiv:2003.1043

Time-sensitive influence maximization in social networks

One of the fundamental issues in social networks is the influence maximization problem, where the goal is to identify a small subset of individuals such that they can trigger the largest number of members in the network. In real-world social networks, the propagation of information from a node to another may incur a certain amount of time delay; moreover, the value of information may decrease over time. So not only the coverage size, but also the propagation speed matters. In this paper, we propose the Time-Sensitive Influence Maximization (TSIM) problem, which takes into account the time dependence of the information value. Considering the time delay aspect, we develop two diffusion models, namely the Delayed Independent Cascade model and the Delayed Linear Threshold model. We show that the TSIM problem is NP-hard under these models but the spread function is monotone and submodular. Thus, a greedy approximation algorithm can achieve a 1 − 1/e approximation ratio. Moreover, we propose two time-sensitive centrality measures and compare their performance with the greedy algorithm.We evaluate our methods on four real-world datasets. Experimental results show that the proposed algorithms outperform existing methods, which ignore the decay of information value over time