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RTL Design Flow - Computation Structures Group

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DAG Covering<br />

Sound Algorithmic approach<br />

NP-hard optimization problem<br />

Tree covering heuristic: If subject and primitive<br />

DAGs are trees, efficient algorithm can find<br />

optimum cover in linear time<br />

⇒ dynamic programming formulation<br />

Resulting Trees<br />

multiple fanout<br />

Break at multiple fanout points<br />

25<br />

27<br />

Partitioning a Graph<br />

Dynamic Programming<br />

Principle of optimality: Optimal cover for a tree<br />

consists of a match at the root of the tree<br />

plus the optimal cover for the sub-trees<br />

starting at each input of the match<br />

y<br />

x<br />

p<br />

z<br />

Best cover for<br />

this match uses<br />

best covers for<br />

x, y, z<br />

Best cover for<br />

this match uses<br />

best covers for<br />

p, z<br />

26<br />

28

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