Given a social network G and a positive integer k, the influence maximization problem asks for k nodes (in G) whose adoptions of a certain idea or product can trigger the largest expected number of follow-up adoptions by the remaining nodes This problem has been extensively studied in the literature, and the state-of-the-art technique runs in O((k+l) (n+m) log n e2) expected time and returns a (1-1 e-e)-approximate solution with at least 1 - 1/n l probability This paper presents an influence maximization algorithm that provides the same worst-case guarantees as the state of the art, but offers significantly improved empirical efficiency The core of our algorithm is a set of estimation techniques based on martingales, a classic statistical tool Those techniques not only provide accurate results with small computation overheads, but also enable our algorithm to support a larger class of information diffusion models than existing methods do We experimentally evaluate our algorithm against the states of the art under several popular diffusion models, using real social networks with up to 14 billion edges Our experimental results show that the proposed algorithm consistently outperforms the states of the art in terms of computation efficiency, and is often orders of magnitude faster

Influence Maximization in Near-Linear Time: A Martingale Approach

Given a social network G and a constant k, the influence maximization problem asks for k nodes in G that (directly and indirectly) influence the largest number of nodes under a pre-defined diffusion model. This problem finds important applications in viral marketing, and has been extensively studied in the literature. Existing algorithms for influence maximization, however, either trade approximation guarantees for practical efficiency, or vice versa. In particular, among the algorithms that achieve constant factor approximations under the prominent independent cascade (IC) model or linear threshold (LT) model, none can handle a million-node graph without incurring prohibitive overheads. 
This paper presents TIM, an algorithm that aims to bridge the theory and practice in influence maximization. On the theory side, we show that TIM runs in O((k+\ell) (n+m) \log n / \epsilon^2) expected time and returns a (1-1/e-\epsilon)-approximate solution with at least 1 - n^{-\ell} probability. The time complexity of TIM is near-optimal under the IC model, as it is only a \log n factor larger than the \Omega(m + n) lower-bound established in previous work (for fixed k, \ell, and \epsilon). Moreover, TIM supports the triggering model, which is a general diffusion model that includes both IC and LT as special cases. On the practice side, TIM incorporates novel heuristics that significantly improve its empirical efficiency without compromising its asymptotic performance. We experimentally evaluate TIM with the largest datasets ever tested in the literature, and show that it outperforms the state-of-the-art solutions (with approximation guarantees) by up to four orders of magnitude in terms of running time. In particular, when k = 50, \epsilon = 0.2, and \ell = 1, TIM requires less than one hour on a commodity machine to process a network with 41.6 million nodes and 1.4 billion edges.

Influence Maximization: Near-Optimal Time Complexity Meets Practical Efficiency

Though research on the Semantic Web has progressed at a steady pace, its promise has yet to be realized. One major difficulty is that, by its very nature, the Semantic Web is a large, uncensored system to which anyone may contribute. This raises the question of how much credence to give each source. We cannot expect each user to know the trustworthiness of each source, nor would we want to assign top-down or global credibility values due to the subjective nature of trust. We tackle this problem by employing a web of trust, in which each user maintains trusts in a small number of other users. We then compose these trusts into trust values for all other users. The result of our computation is not an agglomerate "trustworthiness" of each user. Instead, each user receives a personalized set of trusts, which may vary widely from person to person. We define properties for combination functions which merge such trusts, and define a class of functions for which merging may be done locally while maintaining these properties. We give examples of specific functions and apply them to data from Epinions and our BibServ bibliography server. Experiments confirm that the methods are robust to noise, and do not put unreasonable expectations on users. We hope that these methods will help move the Semantic Web closer to fulfilling its promise.

Trust management for the Semantic Web

Given a social network G and a constant $k$, the influence maximization problem asks for k nodes in G that (directly and indirectly) influence the largest number of nodes under a pre-defined diffusion model. This problem finds important applications in viral marketing, and has been extensively studied in the literature. Existing algorithms for influence maximization, however, either trade approximation guarantees for practical efficiency, or vice versa. In particular, among the algorithms that achieve constant factor approximations under the prominent independent cascade (IC) model or linear threshold (LT) model, none can handle a million-node graph without incurring prohibitive overheads. This paper presents TIM, an algorithm that aims to bridge the theory and practice in influence maximization. On the theory side, we show that TIM runs in O((k+ l) (n+m) log n/e2) expected time and returns a (1-1/e-e)-approximate solution with at least 1 - n-l probability. The time complexity of TIM is near-optimal under the IC model, as it is only a log n factor larger than the Ω(m + n) lower-bound established in previous work (for fixed k, l, and e). Moreover, TIM supports the triggering model, which is a general diffusion model that includes both IC and LT as special cases. On the practice side, TIM incorporates novel heuristics that significantly improve its empirical efficiency without compromising its asymptotic performance. We experimentally evaluate TIM with the largest datasets ever tested in the literature, and show that it outperforms the state-of-the-art solutions (with approximation guarantees) by up to four orders of magnitude in terms of running time. In particular, when k = 50, e = 0.2, and l = 1, TIM requires less than one hour on a commodity machine to process a network with 41.6 million nodes and 1.4 billion edges. This demonstrates that influence maximization algorithms can be made practical while still offering strong theoretical guarantees.

Influence maximization: near-optimal time complexity meets practical efficiency

Influence Maximization (IM), which selects a set of $k$ users (called seed set) from a social network to maximize the expected number of influenced users (called influence spread), is a key algorithmic problem in social influence analysis. Due to its immense application potential and enormous technical challenges, IM has been extensively studied in the past decade. In this paper, we survey and synthesize a wide spectrum of existing studies on IM from an algorithmic perspective , with a special focus on the following key aspects: (1) a review of well-accepted diffusion models that capture the information diffusion process and build the foundation of the IM problem, (2) a fine-grained taxonomy to classify existing IM algorithms based on their design objectives, (3) a rigorous theoretical comparison of existing IM algorithms, and (4) a comprehensive study on the applications of IM techniques in combining with novel context features of social networks such as topic, location, and time. Based on this analysis, we then outline the key challenges and research directions to expand the boundary of IM research.

https://ink.library.smu.edu.sg/cgi/viewcontent.cgi?article=4983&context=sis_research

Influence Maximization on Social Graphs: A Survey

As social network services connect people across the world, influence maximization, i.e., finding the most influential nodes (or individuals) in the network, is being actively researched with applications to viral marketing. One crucial challenge in scalable influence maximization processing is evaluating influence, which is #P-hard and thus hard to solve in polynomial time. We propose a scalable influence approximation algorithm, Independent Path Algorithm (IPA) for Independent Cascade (IC) diffusion model. IPA efficiently approximates influence by considering an independent influence path as an influence evaluation unit. IPA are also easily parallelized by simply adding a few lines of OpenMP meta-programming expressions. Also, overhead of maintaining influence paths in memory is relieved by safely throwing away insignificant influence paths. Extensive experiments conducted on large-scale real social networks show that IPA is an order of magnitude faster and uses less memory than the state of the art algorithms. Our experimental results also show that parallel versions of IPA speeds up further as the number of CPU cores increases, and more speed-up is achieved for larger datasets. The algorithms have been implemented in our demo application for influence maximization (available at http://dm.postech.ac.kr/ipa demo), which efficiently finds the most influential nodes in a social network.

Seung-Keol Kim

Papers

Scalable and parallelizable processing of influence maximization for large-scale social networks?

Scalable and parallelizable influence maximization with Random Walk Ranking and Rank Merge Pruning