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By a result of Yannakakis, we know that this problem can be solved deterministically by communicating $O(\log^2 n)$ bits where $n$ is the size of vertex set in $V$. It has been an open problem for a long time whether this upper bound can be improved.

A recent result of Goos, Pitassi and Watson shows that this upper bound is tight, i.e., there is a graph for which the CIS game requires $\tilde{\Omega}(\log^2 n)$ communication. In the talk, we will see proof-sketches of these results.