We formulate a new stochastic submodular maximization problem by introducing the performance-dependent costs of items. In this problem, we consider selecting items for the case where the performance of each item (i.e., how much an item contributes to the objective function) is decided randomly, and the cost of an item depends on its performance. The goal of the problem is to maximize the objective function subject to a budget constraint on the costs of the selected items. We present an adaptive algorithm for this problem with a theoretical guaran-√ tee that its expected objective value is at least (1−1/ 4 e)/2 times the maximum value attained by any adaptive algorithms. We verify the performance of the algorithm through numerical experiments.
Two clusters of the coronavirus disease 2019 (COVID-19) were confirmed in Hokkaido, Japan, in February 2020. To identify these clusters, this study employed web search query logs of multiple devices and user location information from location-aware mobile devices. We anonymously identified users who used a web search engine (i.e., Yahoo! JAPAN) to search for COVID-19 or its symptoms. We regarded them as web searchers who were suspicious of their own COVID-19 infection (WSSCI). We extracted the location of WSSCI via a mobile operating system application and compared the spatio-temporal distribution of WSSCI with the actual location of the two known clusters. In the early stage of cluster development, we confirmed several WSSCI. Our approach was accurate in this stage and became biased after a public announcement of the cluster development. When other cluster-related resources, such as detailed population statistics, are not available, the proposed metric can capture hints of emerging clusters.
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