Abstract
Given a specific propagation speed $h$ in a social network $G(V, E)$ , an influence circle(IC) of a node $s$ in time $t$ is a node set of its influenced nodes, where the distance between $s$ and its expected influenced node $w$ is less than radius $r=ht$ . Different from the Influence Maximization(IM) problem which finds a set of $k$ initial seed nodes in a network so that the expected size of cascade is maximized, the aim of the proposed influence circle covering (ICCovering) problem in this work is to find a minimum number of seeds or ICs to cover the whole network. The general approach for this covering problem is greedy strategy, which iteratively selects a seed with the largest influence circle. However, the upper bound of greedy algorithms does not perform very well, and the value will increase further as the network scale expands. In this paper, we propose an $\alpha $ -approximation partitioning algorithm for large-scale social networks, where $\alpha $ is the maximum number of outer edges of Voronoi cells appeared in the partition. The algorithm divides the input graph into smaller cells so that each cell can be solved separately, and a feasible solution to the input object can be constructed by combining the solutions of the smaller cells. When solving the smaller cells, we adopt the linear programming method. In order to improve its effectiveness and efficiency, we also propose two optimization algorithms. Extensive experiments on real social networks confirm the superiorities and effectiveness of our solution.
Highlights
Given a social network G(V, E), where V denotes the node set and E denotes the directed edge set
An influence circle (IC) of a seed node s in G is defined as a node set where max{d(s, v) | v ∈ V } ≤ r, where r is the radius of the influence circle, represents influence spread in time t with a specific speed h
If the distance from the seed node to the boundary of a Voronoi cell is less than the radius of IC, or that the IC of a seed does not all fall into a Voronoi cell, the seed node is said to be located at the boundary of the cell
Summary
Given a social network G(V, E), where V denotes the node set and E denotes the directed edge set. Based on the observation of the time limit, some papers have raised the issue of time-critical influence maximization, which aims to maximize influence spread within a given deadline [10]–[14] Their proposed models and algorithms cannot ensure that all nodes in the social network have a certain degree of opportunity to be activated within the time limit. The other challenge is relevant social networks for this problem can scale to massive size, even on the order of the million-node graph This further adds difficulty to the influence circle estimating, and brings difficulties – how to obtain an optimal solution of the covering. We have conducted experiments on both small and large-scale networks, and the experimental results strongly corroborate the effectiveness and efficiency of our approach
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