Scheduling unitary task systems with zero–one communication delays for quasi-interval orders Original Research Article

The class of quasi-interval orders contains properly two rich families of precedence graphs: interval orders and a subclass of series–parallel orders. In this paper, we consider the problem of scheduling unitary task systems with zero–one communication delays in order to minimize the total elapsed time for the execution of all the tasks. This problem is known to be NP-complete on an unlimited number of processors even for interval orders. When the precedence constraints are given by a quasi-interval order G and the communication delays are locally identical (which includes the UET-UCT case), we show that an optimal static scheduling can be determined in O(n log n+e) time where n denotes the number of tasks and e denotes the number of the precedence constraints in the transitive closure of G. Some extensions are discussed for nonquasi-interval orders.