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Syst."],"published-print":{"date-parts":[[2020,3,31]]},"abstract":"<jats:p>&lt;?tight?&gt;To increase the resource utilization in multi-FPGA (field-programmable gate array) systems, time-division multiplexing (TDM) is a widely used technique to accommodate a large number of inter-FPGA signals. However, with this technique, the delay imposed by the inter-FPGA connections becomes significant. Previous research has shown that the TDM ratios of signals can greatly affect the performance of a system. In this article, to minimize the system clock period and support more practical constraints in modern multi-FPGA systems, we propose an analytical framework to optimize the TDM ratios of inter-FPGA nets. A Lagrangian relaxation-based method first gives a continuous result under relaxed constraints. A binary search--based discretization algorithm is then used to assign the TDM ratio of each net such that the resulting maximum displacement is optimal and all the constraints are satisfied. Finally, a swapping-based post refinement is performed to further optimize the TDM ratios. For comparison, we also solve the problem using linear programming (LP)--based methods, which have guaranteed error bounds to the optimal solutions. Experimental results show that our framework can achieve similar quality with much shorter runtime compared to the LP-based methods. Moreover, our framework scales for designs with over 45,000 inter-FPGA nets while the runtime and memory usage of the LP-based methods will increase dramatically as the design scale becomes larger.<\/jats:p>","DOI":"10.1145\/3377551","type":"journal-article","created":{"date-parts":[[2020,2,3]],"date-time":"2020-02-03T12:35:17Z","timestamp":1580733317000},"page":"1-23","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":10,"title":["Lagrangian Relaxation-Based Time-Division Multiplexing Optimization for Multi-FPGA Systems"],"prefix":"10.1145","volume":"25","author":[{"given":"Chak-Wa","family":"Pui","sequence":"first","affiliation":[{"name":"The Chinese University of Hong Kong, Hong Kong"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Evangeline F. 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