What algorithmic approach for selecting similar, relevancy based documents
Check out term frequency-inverse document frequency (TF-IDF), if you're parsing large chunks of text for mentioned topics. The metric measures importance of topics bounded by how often they appear across a corpus of documents, which helps to weed out topics that may be very common, but are very common to all discussions, and therefore not very useful.

It's a simple calculation, but there is a ruby gem that calculates it directly: tf-idf-similarity.

Hope this helps.