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Scheduling an Edge The scheduling of an edge eij can be divided into three parts: scheduling on the source processor Psrc , on the links of the route R, and on the destination processor Pdst On the source processor, an edge must be scheduled together with its origin node ni , as the foregoing considerations in the context of the direct scheduling showed Of course, when ni is scheduled, only those leaving edges, whose destination nodes will be executed on a processor other than Psrc , are scheduled on Psrc The scheduling on the links and on the destination processor can take place with either the origin node ni or the destination node nj Hence, there are three alternatives for the scheduling of an edge eij 1 Schedule eij on Psrc with ni , on R, Pdst with nj This alternative is identical to the approach of direct scheduling, where the edge eij is scheduled on the links of R and on the destination processor Pdst , when its destination node nj is scheduled Figure 812 illustrates this alternative, where the nodes A and C of the depicted task graph are allocated to processor P1 , and B and D are allocated to P2 , and they are scheduled in the order A, B, C, D Figure 812(a) shows the intermediate schedule after scheduling B and Figure 812(b) shows the nal schedule 2 Schedule eij on Psrc , R with ni , on Pdst with nj Here, eij is scheduled not only on Psrc , but also on the links, when ni is scheduled This way, the edges are scheduled on the links of R in the scheduling order of their origin nodes, while in the rst alternative the edges are scheduled on the links in the order of their destination nodes Figure 813 demonstrates this difference, by repeating the example of Figure 812, now scheduling eij on the links with the origin node ni So eAD starts earlier than eBC ; in Figure 812 it is the other way around 3 Schedule eij on Psrc , R, Pdst with ni Edge eij is completely scheduled together with its origin node ni This alternative is likely to produce the best scheduling
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Figure 812 Scheduling with given allocation: edge eij scheduled on Psrc with ni , on R, Pdst with nj , as in direct scheduling Node order is A, B, C, D; os,r (e, P) = 05, is,r (e, L) = 075 (e, L)
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Figure 813 Scheduling with given allocation: edge eij scheduled on Psrc , R with ni , on Pdst with nj Node order is A, B, C, D; os,r (e, P) = 05, is,r (e, L) = 075 (e, L)
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alignment of the edge on the source processor, the links and the destination processor, as the scheduling is done in a single step Note that the scheduling of an edge on the processors and links does not require alignment; therefore, it is called the nonaligned approach, but it is obvious that large differences between the scheduling times on the links and the processors are not realistic Hence, in terms of the scheduling of the edge, this alternative is probably the most accurate Unfortunately, it has a similar disadvantage as the direct scheduling of the entering edges: the scheduling of the edges on their destination processors might prevent the ef cient scheduling of the nodes Figure 814 illustrates the previous example, now with the complete scheduling of the edges on all resources with their origin nodes As the edge eAD is scheduled before
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Figure 814 Scheduling with given allocation: edge eij scheduled on Psrc , R, Pdst with ni ; (a) without insertion; (b) with insertion Node order is A, B, C, D; os,r (e, P) = 05, is,r (e, L) = 075 (e, L)
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