We consider the problem `P| it
prec},c_{ij}=1|C_{max}` of scheduling jobs with
arbitrary processing times on m parallel machines
subject to precedence constraints and unit time
communication delays. We show that, given an optimal
schedule on an unlimited number of machines, i.e. for
the problem `P&;| it
prec},c_{ij}=1|C_{max}`, one can construct a job
priority list such that applying priority list
scheduling determines a schedule whose makespan is at
most twice the minimum. When the precedence constraints
are given by a series-parallel order, we derive a
polynomial algorithm to construct such an optimal
schedule on a sufficiently large number of machines,
thus obtaining a simple and fast approximation
algorithm with a worst case performance ratio of at
most two for the problem `P| it
series-parallel}, c_{ij}=1|C_{max}`. The overall
running time of the presented approach is
O(n'+min{nlog n, npmax}) where n'
denotes the number of precedence relations, and n and
pmax denote the number of jobs and the largest
processing time, respectively.
