Abstract
In interconnect optimization by wiresizing, minimizing weighted sink delay has been shown to be the key problem. Wiresizing 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. GWSA, first introduced in [10] for discrete wiresizing and later extended in [2] to continuous wiresizing, is a greedy wiresizing 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%.
Original language  English 

Title of host publication  ISPD '98 
Subtitle of host publication  Proceedings of the 1998 International Symposium on Physical Design 
Publisher  Association for Computing Machinery (ACM) 
Pages  3944 
Number of pages  6 
ISBN (Print)  9781581130218 
DOIs  
Publication status  Published  6 Apr 1998 
Event  1998 International Symposium on Physical Design, ISPD 1998  Monterey, United States Duration: 6 Apr 1998 → 8 Apr 1998 https://dl.acm.org/doi/proceedings/10.1145/274535 (Conference proceedings) 
Publication series
Name  Proceedings of The international Symposium on Physical Design, ISPD 

Symposium
Symposium  1998 International Symposium on Physical Design, ISPD 1998 

Country/Territory  United States 
City  Monterey 
Period  6/04/98 → 8/04/98 
Internet address 

Scopus Subject Areas
 Electrical and Electronic Engineering