Let $P_2 ( G ),\gamma_f ( G )$, and $\gamma ( G )$ be the 2-packing number, fractional domination number, and domination number, respectively, of a graph G. Domke, Hedetniemi, and Laskar [Congress. Numer., 66 (1989), pp. 227–238] showed that $P_2 ( G ) \leq \gamma_f ( G ) \leq \gamma ( G )$. Examples are given with $P_2 ( G ) < \gamma_f ( G ) = \gamma ( G )$ and $P_2 ( G ) = \gamma_f ( G ) < \gamma ( G )$. Let $G \oplus H$ and $G \cdot H$ be the Cartesian product and strong direct product, respectively, of graphs G and H. For all G and H, it is shown that $P_2 ( G )P_2 ( H ) \leq P_2 ( G\cdot H ) \leq P_2 ( G )\gamma_f ( H )$ and $\gamma ( G )\gamma_f ( H ) \leq \gamma ( G\cdot H ) \leq \gamma ( G )\gamma ( H )$. These relations are also independent. Relations involving $P_2 ( G \oplus H ),\gamma_f ( G \oplus H )$, $\gamma ( G \oplus H )$ are examined. An unresolved issue involves a conjecture of Vizing: For all G and H, is $\gamma ( G \oplus H ) \geq \gamma ( G )\gamma ( H )$?

A problem that requires I inputs, K outputs and I computations is to be solved on a d-dimensional parallel processing machine (usually d>