The problem of influence maximization is to select the most influential individuals in a social network. With the popularity of social network sites, and the development of viral marketing, the importance of the problem has been increased. The influence maximization problem is NP-hard, and therefore, there will not exist a polynomial-time algorithm to solve the problem unless P=NP. Many heuristics are proposed to find a nearly good solution in a shorter time. In this paper, we propose two heuristic algorithms to find good solutions. The heuristics are based on two ideas: (1) vertices of high degree have more influence in the network, and (2) nearby vertices influence on almost analogous sets of vertices. We evaluate our algorithms on several well-known data sets and show that our heuristics achieve better results (up to @math in influence spread) for this problem in a shorter time (up to @math improvement in the running time).
Given a social network G and a constant @math , 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 is the problem of finding a small subset of nodes (seed nodes) in a social network that could maximize the spread of influence. In this paper, we study the efficient influence maximization from two complementary directions. One is to improve the original greedy algorithm of [5] and its improvement [7] to further reduce its running time, and the second is to propose new degree discount heuristics that improves influence spread. We evaluate our algorithms by experiments on two large academic collaboration graphs obtained from the online archival database arXiv.org. Our experimental results show that (a) our improved greedy algorithm achieves better running time comparing with the improvement of [7] with matching influence spread, (b) our degree discount heuristics achieve much better influence spread than classic degree and centrality-based heuristics, and when tuned for a specific influence cascade model, it achieves almost matching influence thread with the greedy algorithm, and more importantly (c) the degree discount heuristics run only in milliseconds while even the improved greedy algorithms run in hours in our experiment graphs with a few tens of thousands of nodes. Based on our results, we believe that fine-tuned heuristics may provide truly scalable solutions to the influence maximization problem with satisfying influence spread and blazingly fast running time. Therefore, contrary to what implied by the conclusion of [5] that traditional heuristics are outperformed by the greedy approximation algorithm, our results shed new lights on the research of heuristic algorithms. We live in a world of social networks. Our everyday choices are often influenced by social interactions. Word of mouth, meme diffusion on the Internet, and viral marketing are all examples of how social networks can affect our behaviour. In many practical applications, it is of great interest to determine which nodes have the highest influence over the network, i.e., which set of nodes will, indirectly, reach the largest audience when propagating information. These nodes might be, for instance, the target for early adopters of a product, the most influential endorsers in political elections, or the most important investors in financial operations, just to name a few examples. Here, we tackle the NP-hard problem of influence maximization on social networks by means of a Genetic Algorithm. We show that, by using simple genetic operators, it is possible to find in feasible runtime solutions of high-influence that are comparable, and occasionally better, than the solutions found by a number of known heuristics (one of which was previously proven to have the best possible approximation guarantee, in polynomial time, of the optimal solution). The advantages of Genetic Algorithms show, however, in them not requiring any assumptions about the graph underlying the network, and in them obtaining more diverse sets of feasible solutions than current heuristics. Nowadays, in the world of limited attention, the techniques that maximize the spread of social influence are more than welcomed. Companies try to maximize their profits on sales by providing customers with free samples believing in the power of word-of-mouth marketing, governments and non-governmental organizations often want to introduce positive changes in the society by appropriately selecting individuals or election candidates want to spend least budget yet still win the election. In this work we propose the use of evolutionary algorithm as a mean for selecting seeds in social networks. By framing the problem as genetic algorithm challenge we show that it is possible to outperform well-known greedy algorithm in the problem of influence maximization for the linear threshold model in both: quality (up to 16 better) and efficiency (up to 35 times faster). We implemented these two algorithms by using GPGPU approach showing that also the evolutionary algorithm can benefit from GPU acceleration making it efficient and scaling better than the greedy algorithm. As the experiments conducted by using three real world datasets reveal, the evolutionary approach proposed in this paper outperforms the greedy algorithm in terms of the outcome and it also scales much better than the greedy algorithm when the network size is increasing. The only drawback in the GPGPU approach so far is the maximum size of the network that can be processed - it is limited by the memory of the GPU card. We believe that by showing the superiority of the evolutionary approach over the greedy algorithm, we will motivate the scientific community to look for an idea to overcome this limitation of the GPU approach - we also suggest one of the possible paths to explore. Since the proposed approach is based only on topological features of the network, not on the attributes of nodes, the applications of it are broader than the ones that are dataset-specific. 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 1.4 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. Diffusion is a fundamental graph process, underpinning such phenomena as epidemic disease contagion and the spread of innovation by word-of-mouth. We address the algorithmic problem of finding a set of k initial seed nodes in a network so that the expected size of the resulting cascade is maximized, under the standard independent cascade model of network diffusion. Runtime is a primary consideration for this problem due to the massive size of the relevant input networks. We provide a fast algorithm for the influence maximization problem, obtaining the near-optimal approximation factor of (1--1 e -- e), for any e > 0, in time O((m + n)e-3 log n). Our algorithm is runtime-optimal (up to a logarithmic factor) and substantially improves upon the previously best-known algorithms which run in time Ω(mnk · POLY(e-1)). Furthermore, our algorithm can be modified to allow early termination: if it is terminated after O(β(m + n) log n) steps for some β < 1 (which can depend on n), then it returns a solution with approximation factor O(β). Finally, we show that this runtime is optimal (up to logarithmic factors) for any β and fixed seed size k. Influence maximization is a hard combinatorial optimization problem. It requires the identification of an optimum set of k network vertices that triggers the activation of a maximum total number of remaining network nodes with respect to a chosen propagation model. The problem is appealing because it is provably hard and has a number of practical applications in domains such as data mining and social network analysis. Although there are many exact and heuristic algorithms for influence maximization, it has been tackled by metaheuristic and evolutionary methods as well. This paper presents and evaluates a new evolutionary method for influence maximization that employs a recent genetic algorithm for fixed–length subset selection. The algorithm is extended by the concept of guiding that prevents selection of infeasible vertices, reduces the search space, and effectively improves the evolutionary procedure.