By Topic

Faster minimization of linear wirelength for global placement

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

5 Author(s)
C. J. Alpert ; Res. Lab., IBM Corp., Austin, TX, USA ; T. F. Chan ; A. B. Kahng ; I. L. Markov
more authors

A linear wirelength objective more effectively captures timing, congestion, and other global placement considerations than a squared wirelength objective. The GORDIAN-L cell placement tool minimizes linear wirelength by first approximating the linear wirelength objective by a modified squared wirelength objective, then executing the following loop-(1) minimize the current objective to yield some approximate solution and (2) use the resulting solution to construct a more accurate objective-until the solution converges. This paper shows how to apply a generalization of an algorithm due to Weiszfeld (1937) to placement with a linear wirelength objective and that the main GORDIAN-L loop is actually a special case of this algorithm. We then propose applying a regularization parameter to the generalized Weiszfeld algorithm to control the tradeoff between convergence and solution accuracy; the GORDIAN-L iteration is equivalent to setting this regularization parameter to zero. We also apply novel numerical methods, such as the primal-Newton and primal-dual Newton iterations, to optimize the linear wirelength objective. Finally, we show both theoretically and empirically that the primal-dual Newton iteration stably attains quadratic convergence, while the generalized Weiszfeld iteration is linear convergent. Hence, primal-dual Newton is a superior choice for implementing a placer such as GORDIAN-L, or for any linear wirelength optimization

Published in:

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  (Volume:17 ,  Issue: 1 )