A Min-Cost Flow Based Detailed Router for FPGAs

Seokjin Lee, Yongseok Cheon, Martin D. F. Wong

Research output: Chapter in book/report/conference proceedingConference proceedingpeer-review

9 Citations (Scopus)


Routing for FPGAs has been a very challenging problem due to the limitation of routing resources. Although the FPGA routing problem has been researched extensively, most algorithms route one net at a time, and it can cause the net-ordering problem.

In this paper, we present a detailed routing algorithm for FPGAs based on min-cost flow computations. Using the min-cost flow approach, our algorithm routes all the nets connected to a common logic module simultaneously. At each stage of the network flow computation, we guarantee optimal result in terms of routability and delay cost. For further improvement, we adopt an iterative refinement scheme based on the Lagrangian relaxation technique. The Lagrangian relaxation approach transforms the routing problem into a sequence of Lagrangian subproblems. At each iteration of the algorithm, Lagrangian subproblems are solved by our min-cost flow based routing algorithm. Any violation of congestion constraints is reflected in the value of corresponding Lagrangian multiplier. The Lagrangian multipliers are incorporated into the cost of each routing rosource node and guide the router.

Because our min-cost flow based algorithm minimizes cost function while it maximizes the flow, our algorithm finds congestion-free routing solutions with minimum total delay. Comparison with VPR router shows that our router uses less or equal number of routing tracks with smaller critical path delay as well as total routing delay.

Original languageEnglish
Title of host publicationProceedings of The IEEE/ACM International Conference on Computer-Aided Design, ICCAD 2003
Place of PublicationUnited States
Number of pages6
ISBN (Print)9781581137620
Publication statusPublished - Nov 2003
Event2003 IEEE/ACM International Conference on Computer-Aided Design, ICCAD 2003 - DoubleTree Hotel, San Jose, United States
Duration: 9 Nov 200313 Nov 2003
https://ieeexplore.ieee.org/xpl/conhome/8895/proceeding (Conference proceedings)

Publication series

NameProceedings of the IEEE/ACM international conference on Computer-aided design, ICCAD
ISSN (Print)1092-3152


Conference2003 IEEE/ACM International Conference on Computer-Aided Design, ICCAD 2003
Country/TerritoryUnited States
CitySan Jose
Internet address

Scopus Subject Areas

  • Software
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design

User-Defined Keywords

  • FPGA routing
  • Lagrangian relaxation
  • Min-cost flow algorithm


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