On the Network Visibility Problem
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Social media is an attention economy where users are constantly competing for attention in their followers' feeds. Users are likely to elicit greater attention from their followers, their audience, if their posts remain visible at the top of their followers' feeds for a longer period of time. However, this depends on the rate at which their followers receive information in their feeds, which in turn depends on the users their followers follow. Then, who should follow whom to maximize the visibility each user achieve? In this paper, we represent users' posts and feeds using the framework of temporal point processes. Under this representation, the problem reduces to optimizing a non-submodular nondecreasing set function under matroid constraints. Then, we show that the set function satisfies a novel property, ξ-submodularity, which allows a simple and efficient greedy algorithm to enjoy theoretical guarantees. In particular, we prove that the greedy algorithm offers a (1/ξ + 1) approximation factor, where ξ is the strong submodularity ratio, a new measure of approximate submodularity that we are able to bound in our problem. Experiments on both synthetic and real data gathered from Twitter show that our greedy algorithm is able to consistently outperform several baselines.
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