Editing Open Problems:63
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{{Header | {{Header | ||
+ | |title=Submodular Matching Maximization | ||
|source=bertinoro14 | |source=bertinoro14 | ||
|who=Amit Chakrabarti | |who=Amit Chakrabarti | ||
}} | }} | ||
β | |||
β | 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. | + | 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. |
β | 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? |