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Modern social networks bring people together and help facilitate the organization of various group activities. The rapid development of smart wearable devices has also made feasible the extrapolation of their owners' activity habits. Inspired by the recent work by Ai et al. [2], we design a smart and private social activity invitation framework based on historical data from smart devices. Our paradigm aims at helping users organize group activities in a smart and efficient way while finding compromises to satisfy all involved parties. Compared with Ai et al.'s work [2], our framework is more realistic, whereby users report their personal information to the app server, which is used to provide organizing services to registered members. The app server, however, is untrustworthy and could be motivated by factors such as advertising revenue. Therefore, the app may advertise itself by providing aggregate statistical information about current users to attract new users. This creates a dilemma between the existing users' concerns about personal privacy and the app developers' agenda. Our framework ameliorates this conflict by securing existing users' information under a stateof-the-art privacy concept-differential privacy-guaranteeing quality services to existing users, while also allowing the server to give informative answers to new potential users. In addition, the proposed framework encourages less active or isolated users via a new method based on perturbed graphs. Our simulation results demonstrate that the proposed framework performs well.

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The rental housing market plays a critical role in the United States real estate market. In addition, rent changes are also indicators of urban transformation and social phenomena. However, traditional data sources for market rent prediction are often inaccurate or inadequate at covering large geographies. With the development of housing information exchange platforms such as Craigslist, user-generated rental listings now provide big data that cover wide geographies and are rich in textual information. Given the importance of rent prediction in urban studies, this study aims to develop and evaluate models of rental market dynamics using deep learning approaches on spatial and textual data from Craigslist rental listings. We tested a number of machine learning and deep learning models (e.g., convolutional neural network, recurrent neural network) for the prediction of rental prices based on data collected from Atlanta, GA, USA. With textual information alone, deep learning models achieved an average root mean square error (RMSE) of 288.4 and mean absolute error (MAE) of 196.8. When combining textual information with location and housing attributes, the integrated model achieved an average RMSE of 227.9 and MAE of 145.4. These approaches can be applied to assess the market value of rental properties, and the prediction results can be used as indicators of a variety of urban phenomena and provide practical references for home owners and renters.

Given a graph G = (V, E), the 3-path partition problem is to find a minimum collection of vertex-disjoint paths each of order at most 3 to cover all the vertices of V . It is different from but closely related to the well-known 3-set cover problem. The best known approximation algorithm for the 3-path partition problem was proposed recently and has a ratio 13/9. Here we present a local search algorithm and show, by an amortized analysis, that it is a 4/3-approximation. This ratio matches up to the best approximation ratio for the 3-set cover problem.