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A tournament is an orientation of a complete graph. A vertex $v$ controls a vertex $u\neq v$ if there is a directed path of length at most two from $v$ to $u$, and a $\delta$-king is one that controls at least $\delta(n-1)$ vertices. In the query complexity model, each query reveals the orientation of an edge. Shen, Sh...
We study the quantum query complexity of several basic graph problems. 1) We prove a tight $\Theta(n^{3/2})$ bound for finding a maximum-out-degree vertex in an $n$-vertex tournament, resolving a conjecture of Mande, Paraashar, and Saurabh [FSTTCS'23]. 2) Using the same proof idea, we give a direct proof that finding a...
We study exact learning with membership queries for concept classes $\mathcal C\subseteq\{0,1\}^N$, focusing on the relationships among their deterministic, randomized, and quantum query complexities, denoted $\mathsf{D}(\mathcal C)$, $\mathsf{R}(\mathcal C)$, and $\mathsf{Q}(\mathcal C)$, respectively. The two canonic...
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