Budget Minimization with Time and Influence Constraints in Social Network

Abstract

The problem of influence maximization in social network gains increasing attention in recent years. The target is to seek a seed set that maximizes the influence coverage with given budget and infinite time space. However, in many real-world applications, people are eager to achieve the desired influence coverage with limited time and the smallest budget, where we want to find a minimum seed set with constrained time and influence. We refer to the problem as Budget Minimization (BM). The BM problem is much more challenging compared with traditional influence maximization w.r.t. the following reasons: (1) it requires to find both the minimum size of the seed set and the most influential nodes simultaneously, leading to complex and expensive optimization procedure; (2) the estimation of the influence coverage of a given seed set should be accurate enough, since we have to decide whether it can reach the influence threshold exactly. In this paper, we propose an Extended Simulated Annealing on Budget Minimization (ESABM) method to efficiently find the smallest seed set in the considered BM problem. The ESABM method extends the traditional Simulated Annealing (SA) algorithm by importing the ‘delete’ and ‘insert’ operators in addition to the ‘replace’ operator, which is used in the traditional SA algorithm. Based on the operators, some operator selection techniques are proposed with detailed theoretical guarantees. Moreover, since we have to estimate the influence coverage in the ESABM algorithm, we further propose an efficient layered-graph based influence coverage estimation method. Experimental results conducted on five real world data show that our proposed method outperforms the existing state-of-the-art methods in terms of both accuracy and efficiency.