Many current Natural Language Processing [NLP] techniques work well assuming a large context of text as input data. However they become ineffective when applied to short texts such as Twitter feeds. To overcome the issue, we want to find a related newswire document to a given tweet to provide contextual support for NLP tasks. This requires robust modeling and understanding of the semantics of short texts. The contribution of the paper is two-fold: 1. we introduce the Linking-Tweets-to-News task as well as a dataset of linked tweet-news pairs, which can benefit many NLP applications; 2. in contrast to previous research which focuses on lexical features within the short texts (text-to-word information), we propose a graph based latent variable model that models the inter short text correlations (text-to-text information). This is motivated by the observation that a tweet usually only covers one aspect of an event. We show that using tweet specific feature (hashtag) and news specific feature (named entities) as well as temporal constraints, we are able to extract text-to-text correlations, and thus completes the semantic picture of a short text. Our experiments show significant improvement of our new model over baselines with three evaluation metrics in the new task.