The scheduling of task graphs on two identical processors is considere
d. It is assumed that tasks have unit-execution-time, and arcs are ass
ociated with unit-communication-time delays. The problem is to assign
the tasks to the two processors and schedule their execution in order
to minimize the makespan. A quadratic algorithm is proposed to compute
an optimal schedule for a class of series-parallel graphs, called SP1
graphs, which includes in particular in-forests and out-forests.