exact sequence

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exact sequence

[ig′zakt ′sē·kwəns]
(mathematics)
A sequence of homomorphisms with the property that the kernel of each homomorphism is precisely the image of the previous homomorphism.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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In particular, this shows that [Y.sub.A] is not a split sequence.
Since the computation time to find the optimal split sequence is large, a heuristic has been developed.
As we can see, the resulting total quantity of the split sequence of Figure 14(a) is Q(s) + Q(a) + Q(g), and the resulting total quantity of the reduced graph of Figure 14(b) is Q(s) + 2Q(a) + Q(g).
This method computes the best possible node split sequence with respect to the quantity to minimize.
Computing the optimal split sequence (ONS) takes a lot of computation time, usually hours, because it has to cheek all possible split sequences to find the best solution.
There exist multiple split sequences to solve an irreducible graph.
This will increase the number of possible split sequences. It takes much time to compute all possibilities; therefore, a heuristic is constructed that picks a node [n.sub.i] to split with the smallest H ([n.sub.i]) as defined by

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