Difference between revisions of "Open Problems:67"
(Created page with "{{Header |title=Difficult Instance for MaxCut in the Streaming Model |source=bertinoro14 |who=Robert Krauthgamer }} ???") |
|||
| Line 4: | Line 4: | ||
|who=Robert Krauthgamer | |who=Robert Krauthgamer | ||
}} | }} | ||
| − | + | ||
| + | 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 ? | ||
Revision as of 14:12, 29 May 2014
| 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 ?
