Abstract:
The paper presents a priority algorithm for the maximum lateness problem with parallel
identical processors, precedence constraints, and preemptions. The presented algorithm
calculates the priority of each task by constructing a schedule for the set of its successors.
The algorithm is motivated by comparison of its nonpreemptive counterpart with
other algorithms for the problem with unit execution time tasks. It is shown that the
presented algorithm constructs an optimal schedule for the problem with two processors
and arbitrary precedence constraints, and for the problem with an arbitrary number of
processors and precedence constraints in the form of an in-tree. This proof also indicates
that the presented algorithm allows the worst-case performance ratio previously established
for the so-called Muntz-Coffman algorithm for a particular case of the considered
problem where all due dates are zero.
