Simultaneous driver and wire sizing for performance and power optimization
ICCAD '94 Proceedings of the 1994 IEEE/ACM international conference on Computer-aided design
Optimal wiresizing for interconnects with multiple sources
ACM Transactions on Design Automation of Electronic Systems (TODAES)
Fast performance-driven optimization for buffered clock trees based on Lagrangian relaxation
DAC '96 Proceedings of the 33rd annual Design Automation Conference
Optimal non-uniform wire-sizing under the Elmore delay model
Proceedings of the 1996 IEEE/ACM international conference on Computer-aided design
An efficient approach to simultaneous transistor and interconnect sizing
Proceedings of the 1996 IEEE/ACM international conference on Computer-aided design
Performance optimization of VLSI interconnect layout
Integration, the VLSI Journal
Simultaneous buffer and wire sizing for performance and power optimization
ISLPED '96 Proceedings of the 1996 international symposium on Low power electronics and design
Optimal wiresizing under the distributed Elmore delay model
ICCAD '93 Proceedings of the 1993 IEEE/ACM international conference on Computer-aided design
Fast and Exact Simultaneous Gate and Wire Sizing by Lagrangian Relaxation
Fast and Exact Simultaneous Gate and Wire Sizing by Lagrangian Relaxation
ICCD '00 Proceedings of the 2000 IEEE International Conference on Computer Design: VLSI in Computers & Processors
A class of problems for which cyclic relaxation converges linearly
Computational Optimization and Applications
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In interconnect optimization by wire-sizing, minimizing weighted sink delay has been shown to be the key problem. Wire-sizing with many important objectives such as minimizing total area subject to delay bounds or minimizing maximum delay can all be reduced to solving a sequence of weighted sink delay problems by Lagrangian relaxation [1, 3]. GWSA, first introduced in [10] for discrete wire-sizing and later extended in [2] to continuous wire-sizing, is a greedy wire-sizing algorithm for the weighted sink delay problem. Although GWSA has been experimentally shown to be very efficient, no mathematical analysis on its convergence rate has ever been reported. In this paper, we consider GWSA for continuous wire sizing. We prove that GWSA converges linearly to the optimal solution, which implies that the run time of GWSA is linear with respect to the number of wire segments for any fixed precision of the solution. Moreover, we also prove that this is true for any starting solution. This is a surprising result because previously it was believed that in order to guarantee convergence, GWSA had to start from a solution in which every wire segment is set to the minimum (or maximum) possible width. Our result implies that GWSA can use a good starting solution to achieve faster convergence. We demonstrate this point by showing that the minimization of maximum delay using Lagrangian relaxation can be speed up by 57.7%.