Next up in the mini-course on data streams (first two lectures here and here) were lower bounds and communication complexity. The slides are here:

The outline was:

1. Basic Framework: If you have a small-space algorithm for stream problem $Q$, you can turn this into a low-communication protocol for a related communication problem $P$. Hence, a lower bound on the communication required to solve $P$ implies a lower bound on the space required to solve $Q$. Using this framework, we first proved lower bounds for classic stream problems such as selection, frequency moments, and distinct elements via the communication complexity of indexing, disjointness, and Hamming approximation.
2. Information Statistics: So how do we prove communication lower bounds? One powerful method is to analyze the information that is revealed about a player’s input by the messages they send. We first demonstrated this approach via the simple problem of indexing (a neat pedagogic idea courtesy of Amit Chakrabarti) before outlining how the approach would extend to the disjointness problem.
3. Hamming Distance: Lastly, we presented a lower bound on the Hamming approximation problem using the ingenious but simple proof [Jayram et al.]

Tout le monde! Here’s the group photo from this year’s L’Ecole de Printemps d’Informatique Théorique.