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signed to each node. A simple approach would set the weight proportional to the
size of an object and the size of its largest descendant node. However, such a scheme
fails to consider parameters such as the total size and number of children and the
degree of connectivity among related nodes. Therefore, a critical-path algorithm that
uses a more sophisticated set of heuristics in determining the weight of the node is
represented here.
Definition 4. A critical node is a node that has a child with an in-degree greater
than 1.
5.2.1 Load Balancing
5.2.1.1 Critical Node Effect. Allocate a critical node with the high-
est number of children with in-degree > 1 first. Consider the subDAG shown in
Fig. 18 — A , B , and C are all critical nodes. However, A has priority over B and
C (it has precedence over two nodes whereas B and C have precedence over one
node each). Assume that there are two parallel channels. As can be seen from the
figure, regardless of the sizes of A, B , and C , allocating A first results in a better
load balancing.
5.2.1.2 Number of Children with In-Degree 1. Allocate nodes with
the highest number of children with in-degree 1 first. This could free up more nodes
to be allocated in parallel. Consider the allocation shown in Fig. 19 , and the alloca-
F IG . 18. Critical-node effect.
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