Skip to main content
Book cover

Operations Research and Cyber-Infrastructure pp 443–454Cite as

A Provably Good Global Routing Algorithm in Multilayer IC and MCM Layout Designs

  • Conference paper

  • 1304 Accesses

Part of the Operations Research/Computer Science Interfaces book series (ORCS,volume 47)

Abstract

Given a multilayer routing area, we consider the global routing problem of selecting a maximum set of nets, such that every net can be routed entirely in one of the given layers without violating the physical capacity constraints. This problem is motivated by applications in multilayer IC and multichip module (MCM) layout designs. The contribution of this paper is threefold. First, we formulate the problem as an integer linear program (ILP). Second, we modify an algorithm by Garg and Könemann for packing linear programs to obtain an approximation algorithm for the global routing problem. Our algorithm provides solutions guaranteed to be within a certain range of the optimal value, and runs in polynomial-time even if all, possibly exponentially many, Steiner trees are considered in the formulation. Finally, we demonstrate that the complexity of our algorithm can be significantly reduced in the case of identical routing layers.

This is a preview of subscription content, access via your institution.

Chapter
EUR   29.95
Price includes VAT (Netherlands)
  • DOI: 10.1007/978-0-387-88843-9_23
  • Chapter length: 12 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
EUR   189.99
Price includes VAT (Netherlands)
  • ISBN: 978-0-387-88843-9
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
EUR   249.61
Price includes VAT (Netherlands)
Hardcover Book
EUR   249.61
Price includes VAT (Netherlands)
Learn about institutional subscriptions
Fig. 1
Fig. 2

Notes

  1. 1.

    1 A routing layer considered in this paper may, in practice, be implemented as a pair of layers: one for wiring in the x direction, and the other for wiring in the y direction. The problem formulation and algorithm presented in this paper avoids the use of stacked vias between different pairs of layers. However, vias used to connect wires within any pair of layers may be required. These vias are less expensive, and may be minimized in the detailed routing phase. In the sequel, pairs of layers are simply termed “layers”.

  2. 2.

    2 The best known apoproximation guarantee for the minimum Steiner tree problem is 1.55 [17].

References

  1. C. Albrecht, “Gloabal Routing by New Approximation Algorithms for Multicommodity Flow”, IEEE Transactions on Computer Aided Design of Integrated Circuits and Systems, vol. 20, no. 5, pp. 622–632, May 2001.

    CrossRef  Google Scholar 

  2. K. M. Anstreicher,“Towards a Practical Volumetric Cutting Plane Method for Convex Programming”, SIAM Journal on Optimization, vol. 9, pp. 190–206, 1999.

    CrossRef  MathSciNet  Google Scholar 

  3. S. Arora, C. Lund, R. Motwani, M. Sudan and M. Szegedy, “Proof Verification and Hardness of Approximation Problems”, Journal of the Association for Computing Machinery, vol. 45, pp. 501–555, 1998.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. M. Bern and P. Plassmann, “The Steiner Problem with Edge Lengths 1 and 2”, Information Professing Letters, vol. 32, pp. 171–176, 1989.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. C.-C. Chang and J. Cong, “An Efficient Aproach to Multilayer Layer Assignment with an Application to Via Minimization”, IEEE Transactions on Computer Aided Design of Integrated Circuits and Systems, vol. 18, no. 5, pp. 608–620, May 1999.

    CrossRef  Google Scholar 

  6. M. Chlebík and J. Chlebíková, “Approximation Hardness of the Steiner Tree Problem”, Proceedings of the 8th Scandinavian Workshop on Algorithm Theory, SWAT 2002, LNCS 2368, pp. 170–179.

    Google Scholar 

  7. J. Cong, M. Hossain and N.A. Sherwani, “A Provably Good Multilayer Topological Planar Routing Algorithm in IC layout Designs”, IEEE Transactions on Computer Aided Design of Integrated Circuits and Systems, vol. 12, no. 1, pp. 70–78, Jan. 1993.

    CrossRef  Google Scholar 

  8. J. Cong and C.L. Liu, “On the k-Layer Planar Subset and Via Minimization Problems”, IEEE Transactions on Computer Aided Design of Integrated Circuits and Systems, vol. 10, no. 8, pp. 972–981, Aug. 1991.

    CrossRef  Google Scholar 

  9. N. Garg and J. Könemann, “Fast and Simpler Algorithms for Multicommodity Flow and Other Fractional Packing Problems”, SIAM Journal on Computing, vol. 37, no. 2, pp. 630–652, 2007.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. M. Grötschel, L. Lovász and A. Schrijver, “The Ellipsoid Method and Its Consequences in Combinatorial Optimization”, Combinatorica, vol. 1, pp. 169–197, 1981.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. K. Jansen and H. Zhang, “Approximation algorithms for general packing problems and their application to the multicast congestion problem”, Mathematical Programming, vol. 114, no. 1, pp. 183–206, 2008.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. J.M. Kleinberg, “Approximation Algorithms for Disjoint Paths Problems”, Ph.D. Dissertation, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, May 1996.

    Google Scholar 

  13. L.-C. E. Liu and C. Sechen, “Multilayer Chip-Level Global Routing Using an Efficient Graph-Based Steiner Tree Heuristic”, IEEE Transactions on Computer Aided Design of Integrated Circuits and Systems, vol. 18, no. 10, pp. 1442–1451, Oct. 1999.

    CrossRef  Google Scholar 

  14. S.A. Plotkin, D.B. Shmoys and E. Tardos, “Fast Approximation Algorithms for Fractional Packing and Covering Problems”, Mathematics of Operations Research, vol. 2, pp. 257–301, 1995.

    CrossRef  MathSciNet  Google Scholar 

  15. P. Raghavan, “Probabilistic Construction of Deterministic Algorithms: Approximating Packing Integer Programs”, Journal of Computer and System Sciences, vol. 37, pp. 130–143, 1988.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. P. Raghavan and C. D. Thompson, “Randomized Rounding: A Technique for Provably Good Algorithms and Algorithmic Proofs”, Combinatorica vol. 7, no. 4, pp. 365–374, 1987.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. G. Robins and A. Zelikovsky, “Improved Steiner Tree Approximation in Graphs”, Proceedings of the 11th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2000, pp. 770–779.

    Google Scholar 

  18. M. Saad, T. Terlaky, A. Vannelli and H. Zhang, “Packing Trees in Communication Networks”, Journal of Combinatorial Optimization, vol. 16, no. 4, pp. 402–423, 2008.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. J. Xiong and L. He, “Extended Global Routing With RLC Crosstalk Constraints”, IEEE Transactions on Very Large Scale Integration (VLSI) Systems, vol. 13, no. 3, pp. 319–329, March 2005.

    CrossRef  Google Scholar 

  20. N.E. Young, “Randomized Rounding without Solving the Linear Program”, Proceedings of the 6th ACM-SIAM Symposium on Discrete Algorithms, SODA 1995, pp. 170–178.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Sharjah, United Arab Emirates

    Mohamed Saad

  2. Department of Industrial and Systems Engineering, Lehigh University, Bethlehem, PA, USA

    Tamás Terlaky

  3. College of Physical and Engineering Sciences, University of Guelph, Guelph, ON, Canada

    Anthony Vannelli

  4. Canadian Imperial Bank of Commerce, Toronto, ON, Canada

    Hu Zhang

Authors
  1. Mohamed Saad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tamás Terlaky
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Anthony Vannelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hu Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dept. Systems & Computer Engineering, Carleton University, Ottawa, ON, K1S 5B6, Canada

    John W. Chinneck

  2. Maximal Software, Inc., 2111 Wilson Blvd., Arlington, VA, 22201, USA

    Bjarni Kristjansson

  3. Dept. of Mathematical Sciences College of Engineering and Science, Clemson University, 340975, Clemson, SC, 29634, USA

    Matthew J. Saltzman

Rights and permissions

Reprints and Permissions

Copyright information

© 2009 Springer Science+Business Media, LLC

About this paper

Cite this paper

Saad, M., Terlaky, T., Vannelli, A., Zhang, H. (2009). A Provably Good Global Routing Algorithm in Multilayer IC and MCM Layout Designs. In: Chinneck, J.W., Kristjansson, B., Saltzman, M.J. (eds) Operations Research and Cyber-Infrastructure. Operations Research/Computer Science Interfaces, vol 47. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-88843-9_23

Download citation

  • DOI: https://doi.org/10.1007/978-0-387-88843-9_23

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-387-88842-2

  • Online ISBN: 978-0-387-88843-9

  • eBook Packages: Computer ScienceComputer Science (R0)