Journal of the Institute of Electronics Engineers of Korea SD (대한전자공학회논문지SD)

The Institute of Electronics and Information Engineers (대한전자공학회)
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Timing-Driven Routing Method by Applying the 1-Steiner Tree Algorithm

1-Steiner 트리 알고리즘을 응용한 시간 지향 배선 방법

  • Shim, Ho (Samsung Electronics Semiconductor R&D Center Memory CAE Team) ;
  • Rim, Chong-Suck (Dept. of Computer Science and Engineeering, Sogang University)
  • 심호 (삼성전자 반도체 연구소 메모리 CAE 팀) ;
  • 임종석 (서강대학교 컴퓨터학과)
  • Published : 2002.03.01
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Abstract

In this paper, we propose two timing-driven routing algorithms for single-source net and multi-source net as applications of 1-Steiner heuristic algorithm. Using the method of substituting the cost of 1-Steiner heuristic algorithms with interconnection delay, our routing algorithms can route both single-source net and multi-source net which have all critical source-terminal pairs or one critical pair efficiently Our single-source net routing algorithm reduced the average maximum interconnection delay by up to 2.1% as compared with previous single-source routing algorithm, SERT, and 10.6% as compared with SERT-C. and Our multi-source net routing algorithm increased the average maximum interconnection delay by up to 2.7% as compared with MCMD A-tree, but outperforms it by up to average 1.4% when the signal net has only subset of critical node pairs.

본 논문에서는 1-Steiner 휴리스틱 알고리즘을 응용하여 단일 소스 네트와 다중 소스 네트를 배선하는 두 가지 시간 지향(timing-driven) 배선 방법을 제안한다. 이 방법은1-Steiner 휴리스틱 알고리즘의 계산값 (cost)을 지연시간으로 수정한 것으로 이 방법의 특징은 모든 터미널이 임계터미널인 경우와 또 임계터미널이 부분적으로 존재하는 경우의 단일 소스 네트와 다중 소스 네트를 배선하는 데 동시 적용할 수 있다는 점이다. 실험결과 단일 소스를 배선하는 알고리즘은 기존의 SERT와 SERT-C에 비해 지연시간이 각각 평균 2.1%, 10.6% 감소하는 성능을 보였다. 그리고 다중 소스를 배선하는 알고리즘은 기존의 MCMD A-tree 알고리즘과 비교했을 때 모든 소스, 터미널 쌍이 임계쌍(critical pair)일 경우는 최대 지연 시간이 평균 2.7% 증가했지만 부분적인 임계쌍이 존재할 때는 최대 지연 시간이 평균 1.4% 감소하는 유사한 결과를 도출한다.

Keywords

References

  1. A.B. Kahng, G. Robins, 'A New Class of Iterative Steiner Tree Heuristics with Good Performance,' IEEE Trans. Computer-Aided Design, Vol. 11, pp. 893-902, July 1992 https://doi.org/10.1109/43.144853
  2. D. Richards, 'Fast Heuristic Algorithms for Rectilinear Steiner Trees,' Algorithmica 4, pp. 191-207, 1989 https://doi.org/10.1007/BF01553886
  3. J. Cong, C.K. Koh, 'Performance-Driven Interconnect Design Based on Distributed RC Delay Model,' in Proc. ACM/IEEE Design Automat. Conf., 1993, pp. 606-611
  4. K.D. Boese, A.B. Kahng, G. Robins, 'High Performance Routing Trees with Identified Critical Sinks,' in Proc. ACM/IEEE Design Automat. Conf., 1993, pp. 182-187
  5. K.D. Boese, A.B. Kahng, G. Robins, 'Nearoptimal Critical Sink Routing Tree Constructions,' IEEE Trans. Computer-Aided Design, Vol. 14, pp. 1417-1436, Dec. 1995 https://doi.org/10.1109/43.476573
  6. H. Hou, J. Hu, S.S. Sapatnekar, 'Non-Hanan Routing,' IEEE Trans. Computer-Aided Design, V.18, pp. 436-444, April 1999 https://doi.org/10.1109/43.752927
  7. W.C. Elmore, 'The Transient Response of Damped Linear Network with Particular Regard to Wideband Amplifier,' J. Applied Physics, pp. 55-63, 1948 https://doi.org/10.1063/1.1697872
  8. K.D. Boese, A.B. Kahng, B.A. McCoy, G. Robins, 'Fidelity and Near-Optimality of Elmore-Based Routing Constructions,' in Proc. IEEE Intl. Conf. on Computer Design, 1993, pp. 81-84 https://doi.org/10.1109/ICCD.1993.393400
  9. C.J. Alpert, T.C. Hu, J.H. Huang, A.B. Kahng, 'A Direct Combination of The Prim and Dijkstra Constructions for Improved Performance-Driven Routing,' in Proc. IEEE Int. Symp. on Circuits Syst., 1993, pp. 1869-1872 https://doi.org/10.1109/ISCAS.1993.394112
  10. J. Cong, P.H. Madden, 'Performance Driven Routing with Multiple Sources,' IEEE Trans. Computer-Aided Design, V.16, pp. 410-419, April 1997 https://doi.org/10.1109/43.602477
  11. J. Lillis, C.K. Cheng, 'Timing Optimization for Multisource Nets: Characterization and Optimal Repeater Insertion,' IEEE Trans. Computer-Aided Design, V.18, pp. 322-331, March 1999 https://doi.org/10.1109/43.748162
  12. J. Cong, L. He, 'Optimal Wiresizing for Interconnects with Multiple Sources,' ACM Trans. Design Automation of Electronic Systems, Vol. 1, pp. 478-511, Oct. 1996 https://doi.org/10.1145/238997.239018
  13. A.B. Kahng, G. Robins, On Optimal Interconnections for VLSI. Norwell, MA : Kluwer Academic, 1995
  14. M. Garey, D.S. Johnson, 'The Rectilinear Steiner Problem is NP-Complete,' SIAM J. App. Math, 32(4), pp. 826-834, 1977 https://doi.org/10.1137/0132071
  15. M. Hanan, 'On Steiner's Problem with Rectilinear Distance,' SIAM J. App. Math. 14, pp. 255-265, 1966 https://doi.org/10.1137/0114025