The Common Prefix Problem On Trees
  We present a theoretical study of a problem arising in database query optimization, which we call as The Common Prefix Problem. We present a $(1-o(1))$ factor approximation algorithm for this problem, when the underlying graph is a binary tree. We then use a result of Feige and Kogan to show that even on stars, the problem is hard to approximate. 
Sreyash Kenkre, Sundar Vishwanathan