Multilevel full-chip routing for the X-based architecture

As technology advances into the nanometer territory, the interconnect delay has become a first-order effect on chip performance. To handle this effect, the X-architecture has been proposed for high-performance integrated circuits. The X-architecture presents a new way of orienting a chip's microscopic interconnect wires with the pervasive use of diagonal routes. It can reduce the wire-length and via count, and thus improve performance and routability. Furthermore, the continuous increase of the problem size of IC routing is also a great challenge to existing routing algorithms. In this paper, we present the first multilevel framework for full-chip routing using the X-architecture. To take full advantage of the X-architecture, we explore the optimal routing for three-terminal nets on the X-architecture and develop a general X-Steiner tree algorithm based on the Delaunay triangulation approach for the X-architecture. The multilevel routing framework adopts a two-stage technique of coarsening followed by uncoarsening, with a trapezoid-shaped track assignment embedded between the two stages to assign long, straight diagonal segments for wirelength reduction. Compared with the state-of-the-art multilevel routing for the Manhattan architecture, experimental results show that our approach reduced wirelength by 18.7% and average delay by 8.8% with similar routing completion rates and via counts.

[1]  Yao-Wen Chang,et al.  Timing-driven routing for symmetrical-array-based FPGAs , 1998, Proceedings International Conference on Computer Design. VLSI in Computers and Processors (Cat. No.98CB36273).

[2]  Mircea R. Stan,et al.  Non-Manhattan maze routing , 2004, Proceedings. SBCCI 2004. 17th Symposium on Integrated Circuits and Systems Design (IEEE Cat. No.04TH8784).

[3]  A. Kahng,et al.  The Y architecture for on-chip interconnect: analysis and methodology , 2005, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[4]  Jason Cong,et al.  Multilevel approach to full-chip gridless routing , 2001, IEEE/ACM International Conference on Computer Aided Design. ICCAD 2001. IEEE/ACM Digest of Technical Papers (Cat. No.01CH37281).

[5]  Martin Zachariasen,et al.  A new paradigm for general architecture routing , 2004, GLSVLSI '04.

[6]  Jason Cong,et al.  An enhanced multilevel routing system , 2002, IEEE/ACM International Conference on Computer Aided Design, 2002. ICCAD 2002..

[7]  Cheng-Kok Koh,et al.  Manhattan or non-Manhattan?: a study of alternative VLSI routing architectures , 2000, ACM Great Lakes Symposium on VLSI.

[8]  Feng Zhou,et al.  The Y-architecture: yet another on-chip interconnect solution , 2003, ASP-DAC '03.

[9]  Yao-Wen Chang,et al.  Multilevel routing with antenna avoidance , 2004, ISPD '04.

[10]  Yao-Wen Chang,et al.  A novel framework for multilevel routing considering routability and performance , 2002, ICCAD 2002.

[11]  Hai Zhou,et al.  Efficient octilinear steiner tree construction based on spanning graphs , 2004, ASP-DAC 2004: Asia and South Pacific Design Automation Conference 2004 (IEEE Cat. No.04EX753).

[12]  A. Hashimoto,et al.  Wire routing by optimizing channel assignment within large apertures , 1971, DAC '71.

[13]  Chris Coulston Constructing exact octagonal steiner minimal trees , 2003, GLSVLSI '03.

[14]  D. T. Lee,et al.  A Fast Crosstalk- and Performance-Driven Multilevel Routing System , 2003, ICCAD 2003.

[15]  David S. Johnson,et al.  The Complexity of Computing Steiner Minimal Trees , 1977 .

[16]  Jamil Kawa,et al.  Routing resources consumption on M-arch and X-arch , 2004, 2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512).

[17]  Majid Sarrafzadeh,et al.  Pattern routing: use and theory for increasing predictability andavoiding coupling , 2002, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[18]  Steven L. Teig,et al.  The X architecture: not your father's diagonal wiring , 2002, SLIP '02.

[19]  Mark de Berg,et al.  Computational geometry: algorithms and applications , 1997 .

[20]  Joseph R. Shinnerl,et al.  Multilevel Optimization in VLSICAD , 2003 .

[21]  Hai Zhou,et al.  Track assignment: a desirable intermediate step between global routing and detailed routing , 2002, IEEE/ACM International Conference on Computer Aided Design, 2002. ICCAD 2002..

[22]  Andrew B. Kahng,et al.  Highly scalable algorithms for rectilinear and octilinear Steiner trees , 2003, ASP-DAC '03.

[23]  Yao-Wen Chang,et al.  Timing-driven routing for symmetrical array-based FPGAs , 2000, TODE.

[24]  C. Y. Lee An Algorithm for Path Connections and Its Applications , 1961, IRE Trans. Electron. Comput..