Maximising the Quality of Influence
نویسندگان
چکیده
In percolation theory, vertices within a graph have a binary state: either active or inactive. Furthermore, a percolation process decides how activation spreads within the graph. Firstly, we propose and analyse a simple data-driven percolation process in which percolations are preliminarily learnt from a graph with observed percolations. Secondly, we study a problem related to the one solved by Kempe et al. in [1]: given a percolation process, which k vertices should one choose in order to maximise the number of active vertices at the end of process? This question is important in many areas, ranging from viral marketing to the study of epidemic spread. We generalise the problem by considering activations in [0, 1], measuring the “quality” of percolation, and percolation decays along edges in the percolation graph. For a varying cost of activating each vertex, we maximise the total activation whilst keeping within a budget L. The problem can be solved with a greedy algorithm with a guaranteed approximation quality, and furthermore we show its connection to the maximal coverage problem. The resulting algorithm is analysed empirically over predicted percolation graphs on a synthetic dataset and on a real dataset modelling information diffusion within a social network.
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