@Jdlrobson's work on pushipedia demonstrates the value of presenting the user with "trending" articles in terms of number of edits per unit time. While the ultimate goal would be to have push-notifications (in the apps, and web) to receive updates about such trending articles, an intermediate goal would be to create a service endpoint that returns a list of these articles, which a client might poll at a regular interval.

A natural application for this endpoint would be for the Feeds feature in the iOS and Android apps.

Relevant links:
github.com/jdlrobson/wikitrender
http://trending.wmflabs.org