Transformational placement and synthesis
DATE '00 Proceedings of the conference on Design, automation and test in Europe
Proceedings of the 2001 Asia and South Pacific Design Automation Conference
A primal-dual algorithm for minimizing a sum of Euclidean norms
Journal of Computational and Applied Mathematics
Partition-driven standard cell thermal placement
Proceedings of the 2003 international symposium on Physical design
Metrics for structural logic synthesis
Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design
Implementation and extensibility of an analytic placer
Proceedings of the 2004 international symposium on Physical design
An analytic placer for mixed-size placement and timing-driven placement
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
Smoothing method for minimizing the sum of the r largest functions
Optimization Methods & Software
ComPLx: A Competitive Primal-dual Lagrange Optimization for Global Placement
Proceedings of the 49th Annual Design Automation Conference
Sub-quadratic objectives in quadratic placement
Proceedings of the Conference on Design, Automation and Test in Europe
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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