Fast and Near-Optimal Timing-Driven Cell Sizing under Cell Area and Leakage Power Constraints Using a Simplified Discrete Network Flow Algorithm

Algorithm 1

Network flow algorithm for the cell sizing problem for optimizing timing under a given area constraint.

Algorithm FlowSize

(1) Construct a net structure as depicted in Figure 2 for each net in 𝒫_𝛼.

(2) Determine the cost of each arc in the net structures, so that the change in timing cost is accurately incurred by flows through

them.

(3) Connect net structures with net spanning structures that maintain consistency of size selection of common cells across multiple

net structures; see Section 5.2.

(4) Add the shunting structure and an area output arc (Section 5.3) to each net structure to divert flow of amount equal to the

selected size options (nodes) to the area output arc.

(5) Connect area output arcs to the area gathering node that has only one outgoing arc with capacity equal to the area-constraint to

limit total selected cell area (= flow amount into the node).

(6) Determine a valid min-cost flow in the resulting SSG by applying the standard min-cost flow algorithm and

the min-cost/max-flow heuristics (Section 6) iteratively.

(7) Select the size options chosen by the valid min-cost flow as cell sizes to obtain a near-optimal critical path delay for the circuit.