Worst case analysis of decomposed software pipelining for cyclic unitary RCPSP with precedence delays

In this paper we adress a new cyclic problem: finding periodic schedules for unitary resource constrained cyclic scheduling problem. Such resource constraints are characterized by k, the number of types of functional units employed and mx the maximal number of processors of the same type. The main problem is to cope with both precedence delays and resources which make the problem NP-complete in general. A guaranteed approach, called decomposed software pipelining, has been proposed by Gasperoni and Schwiegelshohn, followed by the retiming method by Calland, Darte and Robert to solve the problem for parallel processors and ordinary precedences. We present, in this paper, an extension of this approach to resource-constrained cyclic scheduling problems with precedence delays and we provide an approximation algorithm. Let λ and λopt be respectively the period given by the algorithm and the optimal period. We establish the bound: