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Journal of Computer Science and Technology

, Volume 21, Issue 1, pp 147–152 | Cite as

ACO-Steiner: Ant Colony Optimization Based Rectilinear Steiner Minimal Tree Algorithm

  • Yu HuEmail author
  • Tong Jing
  • Zhe Feng
  • Xian-Long Hong
  • Xiao-Dong Hu
  • Gui-Ying Yan
Article

Abstract

The rectilinear Steiner minimal tree (RSMT) problem is one of the fundamental problems in physical design, especially in routing, which is known to be NP-complete. This paper presents an algorithm, called ACO-Steiner, for RSMT construction based on ant colony optimization (ACO). An RSMT is constructed with ants' movements in Hanan grid, and then the constraint of Hanan grid is broken to accelerate ants' movements to improve the performance of the algorithm. This algorithm has been implemented on a Sun workstation with Unix operating system and the results have been compared with the fastest exact RSMT algorithm, GeoSteiner 3.1 and a recent heuristic using batched greedy triple construction (BGTC). Experimental results show that ACO-Steiner can get a short running time and keep the high performance. Furthermore, it is also found that the ACO-Steiner can be easily extended to be used to some other problems, such as rectilinear Steiner minimal tree avoiding obstacles, and congestion reduction in global routing.

Keywords

rectilinear Steiner minimal tree (RSMT) routing physical design ant colony optimization (ACO) 

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References

  1. 1.
    Carden R C IV, Li J M, Cheng C K. A global router with a theoretical bound on the optimal solution. IEEE Trans. Computer-Aided Design, Feb. 1996, 15: 208–216.CrossRefGoogle Scholar
  2. 2.
    Jing T, Hong X L, Bao H Y, Xu J Y, Gu J. SSTT: Efficient local search for GSI global routing. J. Computer Science and Technology, 2003, 18(5): 632–639.Google Scholar
  3. 3.
    Jing T, Hong X L, Xu J Y, Bao H Y, Cheng C K, Gu J. UTACO: A unified timing and congestion optimization algorithm for standard cell global routing. IEEE Trans. CAD, 2004, 23(3): 358–365.Google Scholar
  4. 4.
    Xiang H, Tang X P, Wong D F. An algorithm for integrated pin assignment and buffer planning. In Proc. ACM/IEEE Design Automation Conf. (DAC), 2002, pp.584–589.Google Scholar
  5. 5.
    Hong X L, Jing T, Xu J Y, Bao H Y, Gu J. CNB: A critical-network-based timing optimization method for standard cell global routing. J. Computer Science and Technology, 2003, 18(6): 732–738.Google Scholar
  6. 6.
    Xu J Y, Hong X L, Jing T, Cai Y C, Gu J. A novel timing-driven global routing algorithm considering coupling effects for high performance circuit design. IEICE Trans. Fundamentals of ECCS, 2003, E86-A(12): 3158–3167.Google Scholar
  7. 7.
    Wang Y, Hong X L, Jing T, Yang Y, Hu X D, Yan G Y. An efficient low-degree RMST algorithm for VLSI/ULSI physical design. Lecture Notes in Computer Science (LNCS)3254 – Integrated Circuits and System Design, Santorini, Greece, Sept. 2004, pp.442–452.Google Scholar
  8. 8.
    Xu J Y, Hong X L, Jing T, Cai Y C, Gu J. An efficient hierarchical timing-driven Steiner tree algorithm for global routing. INTEGRATION, VLSI J., 2003, 35(2): 69–84.CrossRefGoogle Scholar
  9. 9.
    Garey M R, Johnson D S. The rectilinear Steiner tree problem is NP-complete. SIAM Journal on Applied Mathematics, 1977, 32: 826–834.MathSciNetGoogle Scholar
  10. 10.
    Hwang F K, Richards D S, Winter P. The Steiner Tree Problem, Annals of Discrete Mathematics. Amsterdam: North-Holland, The Netherlands, 1992.Google Scholar
  11. 11.
    Kahng A B, Robins G. A new class of iterative Steiner tree heuristics with good performance. IEEE Trans. Computer-Aided Design, July 1992, 11: 893–902,Google Scholar
  12. 12.
    Borah M, Owens R M, Irwin M J. An edge-based heuristic for Steiner routing. IEEE Trans. Computer Aided Design, 1994, 13: 1563–1568.Google Scholar
  13. 13.
    Kahng A B, Mandoiu I I, Zelikovsky A Z. Highly scalable algorithms for rectilinear and octilinear Steiner trees. In Proc. Asia and South Pacific Design Automation Conference (ASP-DAC), Kitakyushu, Japan, 2003, pp.827–833.Google Scholar
  14. 14.
    Zhou H. Efficient Steiner tree construction based on spanning graphs. In Proc. ACM ISPD, Monterey, CA, USA, 2003, pp.152–157.Google Scholar
  15. 15.
    Qi Zhu, Hai Zhou, Tong Jing, Xianlong Hong, Yang Yang. Spanning graph-based nonrectilinear Steiner tree algorithms. IEEE Trans. CAD, 2005, 24(7): 1066–1075.Google Scholar
  16. 16.
    Warme D M, Winter P, Zachariasen M. Exact algorithms for plane Steiner tree problems: A computational study. Technical Report DIKU-TR-98/11, Department of Computer Science, University of Copenhagen, April 1998.Google Scholar
  17. 17.
    Zachariasen M. Rectilinear full Steiner tree generation. Technical Report DIKU-TR-97/29, Department of Computer Science, University of Copenhagen, December 1997.Google Scholar
  18. 18.
    Dorigo M, Maniezzo V, Colorni A. The Ant System: Optimization by a colony of cooperating agents. IEEE Trans. Systems, Man, and Cybernetics—Part B, 1996, 26(1): 1–13.Google Scholar
  19. 19.
    Das S, Gosavi S V, Hsu W H, Vaze S A. An ant colony approach for the Steiner tree problem. In Proc. Genetic and Evolutionary Computing Conference, New York City, New York, 2002.Google Scholar
  20. 20.
    Ganley J L. Computing optimal rectilinear Steiner trees: A survey and experimental evaluation. Discrete Applied Mathematics, 1998, 89: 161–171.MathSciNetGoogle Scholar
  21. 21.
    Hanan M. On Steiner's problem with rectilinear distance. SIAM Journal on Applied Mathematics, 1966, 14: 255–265.CrossRefzbMATHMathSciNetGoogle Scholar
  22. 22.
    Yang Y Y, Wing O. Suboptimal algorithm for a wire routing problem. IEEE Trans. Circuit Theory, September 1972, 19: 508–510.MathSciNetGoogle Scholar
  23. 23.
    Ganley J L, Cohoon J P. Routing a multi-terminal critical net: Steiner tree construction in the presence of obstacles. In Proc. IEEE International Symposium on Circuits and Systems, London, UK, 1994, pp.113–116.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  • Yu Hu
    • 1
    • 3
    Email author
  • Tong Jing
    • 1
  • Zhe Feng
    • 1
  • Xian-Long Hong
    • 1
  • Xiao-Dong Hu
    • 2
  • Gui-Ying Yan
    • 2
  1. 1.Department of Computer Science and TechnologyTsinghua UniversityBeijingP.R. China
  2. 2.Institute of Applied MathematicsChinese Academy of SciencesBeijingP.R. China
  3. 3.Electrical Engineering DeparmentUCLALos AngelesU.S.A.

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