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Open Access

A Two-Stage Method for Routing in Field-Programmable Gate Arrays with Time-Division Multiplexing

College of Mathematics and Data Science, Minjiang University, Fuzhou 350116, China
School of Mathematics Science, Nanjing Normal University, Nanjing 210024, China
College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116, China
School of Mathematics Science and Institute of Mathematics, Nanjing Normal University, Nanjing 210024, China
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Abstract

Emerging applications widely use field-programmable gate array (FPGA) prototypes as a tool to verify modern very-large-scale integration (VLSI) circuits, imposing many problems, including routing failure caused by the limited number of connections among blocks of FPGAs therein. Such a shortage of connections can be alleviated through time-division multiplexing (TDM), by which multiple signals sharing an identical routing channel can be transmitted. In this context, the routing quality dominantly decides the performance of such systems, proposing the requirement of minimizing the signal delay between FPGA pairs. This paper proposes algorithms for the routing problem in a multi-FPGA system with TDM support, aiming to minimize the maximum TDM ratio. The algorithm consists of two major stages: (1) A method is proposed to set the weight of an edge according to how many times it is shared by the routing requirements and consequently to compute a set of approximate minimum Steiner trees. (2) A ratio assignment method based on the edge-demand framework is devised for assigning ratios to the edges respecting the TDM ratio constraints. Experiments were conducted against the public benchmarks to evaluate our proposed approach as compared with all published works, and the results manifest that our method achieves a better TDM ratio in comparison.

Keywords

approximation algorithmField-programmable gate array (FPGA) routingtime-division multiplexingminimum Steiner treeexact algorithm

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Tsinghua Science and Technology
Volume 27 Issue 6,
December 2022
Pages 902-911
DOI: 10.26599/TST.2021.9010092
Cite this article:
Huang P, Guo L, Sun L, et al. A Two-Stage Method for Routing in Field-Programmable Gate Arrays with Time-Division Multiplexing. Tsinghua Science and Technology, 2022, 27(6): 902-911. https://doi.org/10.26599/TST.2021.9010092

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Received: 10 July 2021
Revised: 27 September 2021
Accepted: 31 October 2021
Published: 21 June 2022
© The author(s) 2022.

The articles published in this open access journal are distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/).
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