In reduction algorithm, the cross-term step is the crucial step
It removes a node, in that way, reducing the number of nodes one by one
Successive applications of this step finally get you down to one entry and one exit node
The following image shows the situation at an arbitrary node that has been selected for removal:
From the displayed image, one can deduce:
(a+b)(c+d+e) = ac+ad+ae+bc+bd+be
Loop Removal Operations
Reduction Procedure Example
Loop Removal Operations:
There are two methods of looking at the loop-removal operation:
One method is to remove the self-loop and then multiply all outgoing links by z*
Another method id to split the node into two equivalent nodes, call them A and A' and put a link between them whose path expression is Z*
Then remove node A' using step 4 and step 5 to produce outgoing links whose path expressions are Z*X and Z*Y
Loop Removal Operations:
There are two methods of looking at the loop-removal operation:
One method is to remove the self-loop and then multiply all outgoing links by z*
Another method id to split the node into two equivalent nodes, call them A and A' and put a link between them whose path expression is Z*
Then remove node A' using step 4 and step 5 to produce outgoing links whose path expressions are Z*X and Z*Y
Reduction Procedure Example
Let us see by applying this algorithm to the following graph where we remove several nodes in order, that is,
Remove node 8 by steps 4 and 5 to obtain
Let us see by applying this algorithm to the following graph where we remove several nodes in order, that is,
Remove node 8 by steps 4 and 5 to obtain
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