Abstract
We present a new channel routing algorithm in the knock-knee mode that produces for dense problems area-optimal layouts with minimum total wire length and O(n) bends (n number of nets), where the total number of bends is at most d −2 (d density) more than the minimum. The running time is O(n). It thus improves the algorithm in [3] that determines area-optimal layouts with minimum total wire length in O(n2) time, where the number of bends is Ω(n 2). Moreover, this is the first area-optimal layout algorithm with linear running time. The approach we use is completely different from all previously known algorithms. It is based on the notion of cycle graphs introduced in this paper.
supported by the DFG under grant Mö 446/1-3.
Preview
Unable to display preview. Download preview PDF.
References
B.S. Baker, S.N. Bhatt, T. Leighton. An approximation algorithm for Manhattan routing. Advances in Computing Research, Vol. 2, VLSI Theory (ed. F.P. Preparata) JAI Press Inc. (1984) 205–229
M.L. Brady, D.J. Brown. VLSI routing: Four layers suffice. Advances in Computing Research, Vol. 2, VLSI Theory (ed. F.P. Preparata) JAI Press Inc. (1984) 245–257
M. Formann, D. Wagner, F. Wagner. Routing through a dense channel with minimum total wire length. Proc. of the 2 nd Ann. ACM-SIAM Symposium on Discrete Algorithms (1991) 475–482
A. Frank. Disjoint paths in a rectilinear grid. Combinatorica 2 (4) (1982)361–371
T. Gonzales, S. Zheng. Simple Three-layer channel routing algorithms. Proc. of AWOC 88 (ed. J.H. Reif), LNCS 319 (1988) 237–246
R. Kuchem, D. Wagner, F. Wagner. Area-optimal three-layer channel routing. Proc. of the 30 th Ann. Symposium on Foundations of Computer Science (1989) 506–511
W. Lipski, Jr. On the structure of three-layer wirable layouts. Advances in Computing Research, Vol. 2, VLSI Theory (ed. F.P. Preparata) JAI Press Inc. (1984) 231–243
W. Lipski, Jr., F.P. Preparata. A unified approach to layout wirability. Mathematical Systems Theory, Vol. 19 (1987) 189–203
K. Mehlhorn, F.P. Preparata. Routing through a rectangle. J. ACM, Vol. 33, No. 1 (1986) 60–85
F.P. Preparata, W. Lipski, Jr. Optimal three-layer channel routing. IEEE Trans. on Computers, C-33 (5) (1984) 427–437
R.L. Rivest, C.M. Fiduccia. A greedy channel router. Proc. 19th Design Automation Conference (1982) 418–424
M. Sarrafzadeh. Channel routing with provably short wires. IEEE Trans. on Circuits and Systems, CAS-34 (9) (1987) 1133–1135
T. Szymanski. Dogleg channel routing is NP-complete. IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems, CAD-4 (1) (1985) 31–41
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wagner, D. (1991). A new approach to knock-knee channel routing. In: Hsu, WL., Lee, R.C.T. (eds) ISA'91 Algorithms. ISA 1991. Lecture Notes in Computer Science, vol 557. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54945-5_52
Download citation
DOI: https://doi.org/10.1007/3-540-54945-5_52
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54945-1
Online ISBN: 978-3-540-46600-0
eBook Packages: Springer Book Archive