An optimal two-processor scheduling for a class of SWITCH-less program nets with combined OR-nodes

This paper deals with two-processor nonpreemptive scheduling problem for acyclic SWITCH-less program nets including two types of nodes: AND-node and OR-node. Compared with task graphs that are a special case of acyclic SWITCH-less program nets and include only AND-nodes, the multiprocessor scheduling problem of general acyclic SWITCH-less program nets is more complicated. Since multiprocessor scheduling problem for general task graphs is NP-hard, so is for acyclic SWITCH-less program nets generally. In this paper, we suppose the acyclic SWITCH-less program nets satisfy: (i) each AND-node and OR-node have 1 and 0 node firing time, respectively; (ii) each AND-node possesses single input edge. For such a class of acyclic SWITCH-less program nets, we first propose a hybrid priority list L that consists of both dynamic and static sub-lists. Then we prove that, for a given acyclic SWITCH-less program net to be executed by two identical processors, the schedule generated by L is optimal.