Abstract
This paper investigates the influence maximization (IM) problem in social networks under the linear threshold (LT) model. Kempe et al. (ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pp. 137–146, 2003) showed that the standard greedy algorithm, which selects the node with the maximum marginal gain repeatedly, brings a -factor approximation solution to this problem. However, Chen et al. (International Conference on Data Mining, pp. 88–97, 2010) proved that the problem of computing the expected influence spread (EIS) of a node is #P-hard. Therefore, to compute the marginal gain exactly is computational intractable. We step-up on investigating efficient algorithm to compute EIS. We show that the EIS of a node can be computed by finding cycles through it, and we further develop an exact algorithm to compute EIS within a small number of hops and an approximation algorithm to estimate EIS without the hop constraint. Based on the proposed EIS algorithms, we finally develop an efficient greedy based algorithm for IM. We compare our algorithm with some well-known IM algorithms on four real-world social networks. The experimental results show that our algorithm is more accurate than others in finding the most influential nodes, and it is also better than or competitive with them in terms of running time. IM is a big topic in social network analysis. In this paper, we investigate efficient influence spread estimation for IM under the LT model. We develop two influence spread estimation algorithms and a new greedy based algorithm for IM under the LT model. The performance of the proposed algorithms are analyzed theoretically and evaluated through simulations.
Highlights
This paper investigates the influence maximization (IM) problem in social networks under the linear threshold (LT) model
The experimental results show that our algorithm is more accurate than others in finding the most influential nodes, and it is better than or competitive with them in terms of running time
IM is a big topic in social network analysis
Summary
We first present a deterministic algorithm for computing the exact value of σT (v) for the case that T ≤ 4 in the ‘A deterministic algorithm’ section and present a randomized algorithm for estimating σT (v) for T ≥ 5 in the ‘A randomized algorithm’ section. Let G be a weighted directed graph; computing σT (v) for all the nodes in G requires O(n T ) time if we use the above simple path method [15], where n denotes the number of nodes in G. Based on Theorem 2, we describe our randomized algorithm for computing σT (v) for all the nodes v ∈ V It runs in O(nT + nr) time, where r is a constant and does not depend on the input graph. Given a weighted directed graph G(V , E, w), the standard greedy algorithm will run EISE O(n) times to select a seed, where n denotes the number of nodes. Algorithm 4 searches the simple paths of length T starting from v and updates the active probability of a node ij according to step 5, in which j−1 l=0 w(il.
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