Difference between revisions of "Open Problems:63"
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| − | Let $G = (V, E)$ be a graph. Fix a monotone submodular function $f : 2^E \rightarrow \mathbb{R}$. A maximum submodular matching $M$ is a subset of $E$ that forms a matching and maximizes $f(E)$. | + | Let $G = (V, E)$ be a graph. Fix a monotone submodular function $f : 2^E \rightarrow \mathbb{R}$. A maximum submodular matching $M$ is a subset of $E$ that forms a matching and maximizes $f(E)$. Suppose the graph edges are streaming. It is known that we cannot compute a maximum weight matching in one pass and $n \operatorname{polylog}(n)$ space to a better approximation than $\frac{e}{e-1}$. Can we show a stronger lower bound for maximum ''submodular'' matchings? A conjecture is that it will be hard to get a better than 2-approximation in one pass with the same space constraints. |
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| − | Suppose the graph edges are streaming. It is known that we cannot compute a maximum weight matching in one pass and $n \operatorname{polylog}(n)$ space to a better approximation than $\frac{e}{e-1}$. Can we show a stronger lower bound for maximum ''submodular'' matchings? | ||
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| − | A conjecture is that it will be hard to get a better than 2-approximation in one pass with the same space constraints. | ||
A related question (due to Deeparnab Chakrabarty): Is there an instance-wise gap between MWMs and MSMs in the stream setting? | A related question (due to Deeparnab Chakrabarty): Is there an instance-wise gap between MWMs and MSMs in the stream setting? | ||
Revision as of 04:16, 4 June 2014
| Suggested by | Amit Chakrabarti |
|---|---|
| Source | Bertinoro 2014 |
| Short link | https://sublinear.info/63 |
Let $G = (V, E)$ be a graph. Fix a monotone submodular function $f : 2^E \rightarrow \mathbb{R}$. A maximum submodular matching $M$ is a subset of $E$ that forms a matching and maximizes $f(E)$. Suppose the graph edges are streaming. It is known that we cannot compute a maximum weight matching in one pass and $n \operatorname{polylog}(n)$ space to a better approximation than $\frac{e}{e-1}$. Can we show a stronger lower bound for maximum submodular matchings? A conjecture is that it will be hard to get a better than 2-approximation in one pass with the same space constraints.
A related question (due to Deeparnab Chakrabarty): Is there an instance-wise gap between MWMs and MSMs in the stream setting?
