9 problems

Optimality conjecture. Under these assumptions, the algorithm used in the proof of Theorem uj1 is optimal for $m=1$. The preceding discussion indicates that the algorithm seems opt…

GPTA optimality conjecture. Among all nested testing procedures that preserve the order $u_1,u_2,\ldots,u_n$, the GPTA is an optimal nested procedure. It is not necessarily uniquel…

Erdős–Frankl–Füredi conjecture.

Let $x$ be the prevalence of a condition in a homogeneous population, let $\gamma_1$ be the threshold at which the elementary algorithm $\mathcal A_1$ becomes dominant, and let…

Sample-complexity conjecture. For any monotone test function $f(\cdot)$,

Hu–Hwang–Wang cutoff-point conjecture. For $r\leq 3$,

Let $p\binom{}{}$ be the prevalence parameter, let $D_k(m,p)$ denote the cost of a nested strategy $(k,m)$, and let $m_{33}$ and $m_{34}$ be the strategies defined by … and … A str…

Consider either combinatorial nonadaptive group testing, where $k$ uniformly randomly chosen items among $n$ are defective, or probabilistic nonadaptive group testing, where each o…

All-colluders-caught estimate. With probability at least $1-\varepsilon_1$, no innocent users are accused, and with probability at least $1-\varepsilon_2$, all colluders are caught…