Problem 65: Communication Complexity of Connectivity
Revision as of 23:00, 13 June 2014 by Krzysztof Onak (talk | contribs) (Krzysztof Onak moved page Waiting:Andrew McGregor2 to Open Problems:65)
| Suggested by | Andrew McGregor |
|---|---|
| Source | Bertinoro 2014 |
| Short link | https://sublinear.info/65 |
A recent result in graph sketching [AhnGM-12] can be rephrased in terms of a simultaneous message communication protocol with public coins. Specifically, suppose that $n$ players are each given a row of the adjacency matrix of some graph. The players simultaneously send a message to a central player who must then determine whether the graph is connected. Existing work shows that this is possible with $O(\log^3 n)$ bit messages from each player. Are $O(\log^2 n)$ or $O(\log n)$ bits sufficient? Also, is there a non-trivial lower bound if the players must use private coins?
