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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
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.
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.
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.
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.
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.
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.
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.
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.
Garey M R, Johnson D S. The rectilinear Steiner tree problem is NP-complete. SIAM Journal on Applied Mathematics, 1977, 32: 826–834.
Hwang F K, Richards D S, Winter P. The Steiner Tree Problem, Annals of Discrete Mathematics. Amsterdam: North-Holland, The Netherlands, 1992.
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,
Borah M, Owens R M, Irwin M J. An edge-based heuristic for Steiner routing. IEEE Trans. Computer Aided Design, 1994, 13: 1563–1568.
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.
Zhou H. Efficient Steiner tree construction based on spanning graphs. In Proc. ACM ISPD, Monterey, CA, USA, 2003, pp.152–157.
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.
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.
Zachariasen M. Rectilinear full Steiner tree generation. Technical Report DIKU-TR-97/29, Department of Computer Science, University of Copenhagen, December 1997.
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.
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.
Ganley J L. Computing optimal rectilinear Steiner trees: A survey and experimental evaluation. Discrete Applied Mathematics, 1998, 89: 161–171.
Hanan M. On Steiner's problem with rectilinear distance. SIAM Journal on Applied Mathematics, 1966, 14: 255–265.
Yang Y Y, Wing O. Suboptimal algorithm for a wire routing problem. IEEE Trans. Circuit Theory, September 1972, 19: 508–510.
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was partially supported by the National Natural Science Foundation of China (NSFC) under Grant No. 60373012, and the Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP) of China under Grant No. 20050003099.
Some preliminary results of this work were presented at IEEE International Conference on Communications, Circuits and Systems (ICCCAS), Chengdu, China, 2004.
Rights and permissions
About this article
Cite this article
Hu, Y., Jing, T., Feng, Z. et al. ACO-Steiner: Ant Colony Optimization Based Rectilinear Steiner Minimal Tree Algorithm. J Comput Sci Technol 21, 147–152 (2006). https://doi.org/10.1007/s11390-006-0147-0
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11390-006-0147-0