A length-matching routing algorithm for high-performance printed circuit boards

Muhammet Mustafa Ozdal, Martin D.F. Wong

Research output: Contribution to journalArticlepeer-review


As the clock frequencies used in industrial applications increase, the timing requirements imposed on routing problems become tighter. Therefore, it becomes important to route the nets within tight minimum and maximum length bounds. Although the problem of routing nets to satisfy maximum length constraints is a well-studied problem, there exists no sophisticated algorithm in literature that ensures that minimum length constraints are also satisfied. In this paper, the authors propose a novel algorithm that effectively incorporates the min-max length constraints into the routing problem. The approach is to use a Lagrangian-relaxation (LR) framework to allocate extra routing resources around nets simultaneously during routing them. The authors also propose a graph model that ensures that all the allocated routing resources can be used effectively for extending lengths. Their routing algorithm automatically prioritizes resource allocation for shorter nets and length minimization for longer nets so that all nets can satisfy their min-max length constraints. This paper demonstrates that this algorithm is effective even in the cases where length constraints are tight, and the spacing between adjacent nets is small.

Original languageEnglish (US)
Pages (from-to)2784-2793
Number of pages10
JournalIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Issue number12
StatePublished - Dec 2006


  • Algorithms
  • Lagrangian relaxation
  • Printed circuit board (PCB)
  • Routing
  • Very large scale integration (VLSI)

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering


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