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A Fully Polynomial Time Approximation Scheme for Timing Driven Minimum Cost Buffer Insertion
, 2009
"... As VLSI technology enters the nanoscale regime, interconnect delay has become the bottleneck of the circuit timing. As one of the most powerful techniques for interconnect optimization, buffer insertion is indispensable in the physical synthesis flow. Buffering is known to be NPcomplete and existin ..."
Abstract

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As VLSI technology enters the nanoscale regime, interconnect delay has become the bottleneck of the circuit timing. As one of the most powerful techniques for interconnect optimization, buffer insertion is indispensable in the physical synthesis flow. Buffering is known to be NPcomplete and existing works either explore dynamic programming to compute optimal solution in the worstcase exponential time or design efficient heuristics without performance guarantee. Even if buffer insertion is one of the most studied problems in physical design, whether there is an efficient algorithm with provably good performance still remains unknown. This work settles this open problem. In the paper, the first fully polynomial time approximation scheme for the timing driven minimum cost buffer insertion problem is designed. The new algorithm can approximate the optimal buffering solution within a factor of 1 + ɛ running in O(m 2 n 2 b/ɛ 3 + n 3 b 2 /ɛ) time for any 0 <ɛ<1, where n is the number of candidate buffer locations, m is the number of sinks in the tree, and b is the number of buffers in the buffer library. In addition to its theoretical guarantee, our experiments on 1000 industrial nets demonstrate that compared to the commonlyused dynamic programming algorithm, the new algorithm well approximates the optimal solution, with only 0.57 % additional buffers and 4.6 × speedup. This clearly demonstrates the practical value of the new algorithm.
Timing Budgeting under Arbitrary Process Variations ∗
"... Timing budgeting under process variations is an important step in a statistical optimization flow. We propose a novel formulation of the problem where budgets are statistical instead of deterministic as in existing works. This new formulation considers the changes of both the means and variances of ..."
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Timing budgeting under process variations is an important step in a statistical optimization flow. We propose a novel formulation of the problem where budgets are statistical instead of deterministic as in existing works. This new formulation considers the changes of both the means and variances of delays, and thus can reduce the timing violation introduced by ignoring the changes of variances. We transform the problem to a linear programming problem using a robust optimization technique. Our approach can be used in latestage design where the detailed distribution information is known, and is most useful in earlystage design since our approach does not assume specific underlying distributions. In addition, with the help of blocklevel timing budgeting, our approach can reduce the timing pessimism. Our approach is applied to the leakage power minimization problem. The results demonstrate that our approach can reduce timing violation from 690ps to 0ps, and the worst total leakage power by 17.50 % on average. 1