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| {{Header | | {{Header |
| + | |title=Title of the problem |
| |source=baltimore16 | | |source=baltimore16 |
| |who=Qin Zhang | | |who=Qin Zhang |
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− | For $\varepsilon\in(0,1]$ and $n\geq 1$, consider the following communication complexity problem $\mathrm{SIJ}_{n,\varepsilon}$: Alice and Bob are given matrices $A,B\in\{0,1\}^{n\times n}$, respectively, and wish to output a $(1+\varepsilon)$-approximation to the number of non-zero entries in the product $C=AB$.
| + | The open problem will appear here. |
− | What is the two-way randomized communication complexity $R_\delta(\mathrm{SIJ}_{n,\varepsilon})$ (where $\delta$ is the probability of error)?
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− | Known facts {{cite|GuchtWWZ-15}}:
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− | * $R^{\to}_{1/n}(\mathrm{SIJ}_{n,\varepsilon}) = \tilde{O}(\frac{n}{\varepsilon^2})$ (one-way communication),
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− | * $R_\delta(\mathrm{SIJ}_{n,\varepsilon}) = \Omega(\frac{n}{\varepsilon^{2/3}})$ for some absolute constant $\delta > 0$.
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− | What is the right dependence on $\varepsilon$?
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− | '''Note:''' $\mathrm{SIJ}$ stands for “Set-Intersection Join,” which is the motivation for this question.
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