In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Input: Consider Input: We study truthful mechanisms for matching and related problems in a partial information<lb>setting, where the agents' true utilities are hidden, and the algorithm only has access to ordi-<lb>nal preference information. Our model is motivated by the fact that in many settings, agents<lb>cannot express the numerical values of their utility for different outcomes, but are still able<lb>to rank the outcomes in their order of preference. Specifically, we study problems where the<lb>ground truth exists in the form of a weighted graph of agent utilities, but the algorithm can<lb>only elicit the agents' private information in the form of a preference ordering for each agent<lb>induced by the underlying weights. Against this backdrop, we design truthful algorithms to<lb>approximate the true optimum solution with respect to the hidden weights. Our techniques<lb>yield universally truthful algorithms for a number of graph problems: a 1.76-approximation<lb>algorithm for Max-Weight Matching, 2-approximation algorithm for Max k-matching, a 6-<lb>approximation algorithm for Densest k-subgraph, and a 2-approximation algorithm for Max<lb>Traveling Salesman as long as the hidden weights constitute a metric. We also provide im-<lb>proved approximation algorithms for such problems when the agents are not able to lie about<lb>their preferences. Our results are the first non-trivial truthful approximation algorithms for<lb>these problems, and indicate that in many situations, we can design robust algorithms even<lb>when the agents may lie and only provide ordinal information instead of precise utilities.

Output: Truthful Mechanisms for Matching and Clustering in an Ordinal World

Input: Consider Input: This papers shows that using separators, which is a pair of two complementary contractors, we can easily and efficiently solve the localization problem of a robot with sonar measurements in an unstructured environment. We introduce separators associated with the Minkowski sum and the Minkowski difference in order to facilitate the resolution. A test-case is given in order to illustrate the principle of the approach.

Output: Minkowski Operations of Sets with Application to Robot Localization

Input: Consider Input: Over the past decade humans have experienced exponential growth in the use of online resources, in particular social media and microblogging websites such as Facebook, Twitter, YouTube and also mobile applications such as WhatsApp, Line, etc. Many companies have identified these resources as a rich mine of marketing knowledge. This knowledge provides valuable feedback which allows them to further develop the next generation of their product. In this paper, sentiment analysis of a product is performed by extracting tweets about that product and classifying the tweets showing it as positive and negative sentiment. The authors propose a hybrid approach which combines unsupervised learning in the form of K-means clustering to cluster the tweets and then performing supervised learning methods such as Decision Trees and Support Vector Machines for classification.
Output: Improved Twitter Sentiment Prediction through 'Cluster-then-Predict Model'