Problem 67: Difficult Instance for Max-Cut in the Streaming Model
| Suggested by | Robert Krauthgamer |
|---|---|
| Source | Bertinoro 2014 |
| Short link | https://sublinear.info/67 |
Let $G$ be a graph consisting of a cycle of length $n$ and a random matching. It is known that this graph is
- an expander
- not bipartite
Let $G'$ be a graph consisting of a cycle of length $n$ and a random matching, with the constraint that the matching must consist only of "even chords": these are chords that are an even number of vertices apart on the cycle. It is easy to see now that this graph is bipartite.
We can say two more things about $G$ and $G'$.
- $G$ is very far from being bipartite:
- $G$ has a max cut of size $n$ and $G'$ does not have a max cut bigger than (say) $0.99n$.
How much space is required to distinguish between these two graphs in a streaming setting ?
