9 problems

Critical-region conjecture. The critical regions are characterized by the equation

Linear speed-up conjecture. When the number of processors is at most

Let $d$ be the dimension and let $\varepsilon$ satisfy … Consider highly parallel algorithms for non-smooth convex optimization, where depth measures the number of sequential compu…

Let $d$ be the dimension, $\varepsilon$ the target accuracy, $K$ the number of queries per parallel round, and $\gamma$ the parameter appearing in the low-dimensional complexity re…

Let $d$ be the dimension, $\varepsilon$ the target accuracy, and $K$ the number of queries made in each parallel round for nonsmooth Lipschitz-continuous optimization over the…

Consider the step-wise odd-even algorithm depicted in Figure, and let $N$ denote the number of elements being sorted. Its sequential worst-case runtime is compared with Bubble Sort…

Let $G$ be a directed graph whose vertices are ordered by a permutation, and let Algorithm be the parallel greedy algorithm that repeatedly identifies vertices with no residual inc…

The asymptotic optimal processor-ratio conjecture. It is conjectured that

Communication-optimality conjecture. These algorithms are all communication-optimal.