A Greedy Descent Method for Budget Constrained Continuous Influence Maximization in Online Social Network

Continuous influence maximization (CIM) in social networks aims to maximize the expected influence spreading by assigning each user a continuous weight reflecting the likelihood and cost for him becoming a seed. Traditional CIM assumes a budget constrain to limit the total cost of all users. However, this assumption does not tenable in practical applications. In practice, it is not necessary to incur costs for all the users. Instead, the budget should be set only for the cost associated with the seed set. In this article, an extended CIM problem of cost distribution under budget (CDB) is defined, which aims to assign different costs to the customers according to their ability to spread influence, ensuring that the cost of each potential seed set does not exceed the budget, while the expected spreading of the product’s influence is maximized. The NP-hardness of CDB and the monotonicity and submodularity of its objective function are investigated. We formulate the CDB problem into a constrained optimization, and present a greedy descent-based algorithm for the problem. In each iteration of the greedy descent method, the influence increment of each node is calculated according to its estimated influence spreading range. The cost distribution is updated along the direction with the maximum increment. The optimal cost distribution can be obtained after several iterations. Precision of the results obtained by the proposed algorithm is analyzed. To avoid the time-consuming simulations, we design an effective algorithm for estimating the seed influence spreading range. Experiment results on real and synthetic networks show that the proposed algorithm can significantly improve the expected influence spreading.