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Electronic Colloquium on Computational Complexity

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REPORTS > KEYWORD > MULTISELECTION:
Reports tagged with Multiselection:
TR23-113 | 8th August 2023
Justin Holmgren, Ron Rothblum

Linear-Size Boolean Circuits for Multiselection

We study the circuit complexity of the multiselection problem: given an input string $x \in \{0,1\}^n$ along with indices $i_1,\dots,i_q \in [n]$, output $(x_{i_1},\dots,x_{i_q})$. A trivial lower bound for the circuit size is the input length $n + q \cdot \log(n)$, but the straightforward construction has size $\Theta(q \cdot n)$.

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