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Open AccessArticle

ParaLarPD: Parallel FPGA Router Using Primal-Dual Sub-Gradient Method

1
Computational Science and Engineering Laboratory, Indian Institute of Technology Indore, Indore 453552, India
2
Electrical and Computer Engineering, National University of Singapore, Singapore 117583, Singapore
3
Center for Advancing Electronics, Technische Universität Dresden, 01062 Dresden, Germany
*
Author to whom correspondence should be addressed.
Electronics 2019, 8(12), 1439; https://doi.org/10.3390/electronics8121439
Received: 25 September 2019 / Revised: 25 November 2019 / Accepted: 27 November 2019 / Published: 1 December 2019
(This article belongs to the Section Circuit and Signal Processing)
In the field programmable gate array (FPGA) design flow, one of the most time-consuming steps is the routing of nets. Therefore, there is a need to accelerate it. In a recent work by Hoo et al., the authors have developed a linear programming (LP)-based framework that parallelizes this routing process to achieve significant speed-ups (the resulting algorithm is termed as ParaLaR). However, this approach has certain weaknesses. Namely, the constraints violation by the solution and a standard routing metric could be improved. We address these two issues here. In this paper, we use the LP framework of ParaLaR and solve it using the primal–dual sub-gradient method that better exploits the problem properties. We also propose a better way to update the size of the step taken by this iterative algorithm. We call our algorithm as ParaLarPD. We perform experiments on a set of standard benchmarks, where we show that our algorithm outperforms not just ParaLaR but the standard existing algorithm VPR as well. We perform experiments with two different configurations. We achieve 20 % average improvement in the constraints violation and the standard metric of the minimum channel width (both of which are related) when compared with ParaLaR. When compared to VPR, we get average improvements of 28 % in the minimum channel width (there is no constraints violation in VPR). We obtain the same value for the total wire length as by ParaLaR, which is 49 % better on an average than that obtained by VPR. This is the original metric to be minimized, for which ParaLaR was proposed. Next, we look at the third and easily measurable metric of critical path delay. On an average, ParaLarPD gives 2 % larger critical path delay than ParaLaR and 3 % better than VPR. We achieve maximum relative speed-ups of up to seven times when running a parallel version of our algorithm using eight threads as compared to the sequential implementation. These speed-ups are similar to those as obtained by ParaLaR. View Full-Text
Keywords: linear programming; lagrangian relaxation; sub-gradient method; optimization; FPGA routing linear programming; lagrangian relaxation; sub-gradient method; optimization; FPGA routing
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Agrawal, R.; Ahuja, K.; Hau Hoo, C.; Duy Anh Nguyen, T.; Kumar, A. ParaLarPD: Parallel FPGA Router Using Primal-Dual Sub-Gradient Method. Electronics 2019, 8, 1439.

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