Abstract
We propose the first theoretical approach to global routing that takes coupling between adjacent wires, bounds on delays along critical paths, and overall capacitance (power consumption) into account. It consists of an efficient combinatorial fully polynomial approximation scheme to a fractional relaxation, followed by randomized rounding. The overall deviation from the optimum can be bounded. The model could also be used for routing traffic flows with congestion-dependent travel times.
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References
Albrecht, C.: Global routing by new approximation algorithms for multicommodity flow. IEEE Transactions on Computer Aided Design of Integrated Circuits and Systems 20, 622–632 (2001a)
Albrecht, C.: Zwei kombinatorische Optimierungsprobleme im VLSIDesign: Optimierung der Zykluszeit und der Slackverteilung und globale Verdrahtung. Ph.D. thesis, University of Bonn (2001b)
Albrecht, C., Korte, B., Schietke, J., Vygen, J.: Maximum mean weight cycle in a digraph and minimizing cycle time of a logic chip. Discrete Applied Mathematics 123, 103–127 (2002)
Carden IV, R.C., Li, J., Cheng, C.-K.: A global router with a theoretical bound on the optimum solution. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 15, 208–216 (1996)
Chernoff, H.: A measure of asymptotic efficiency for tests based on the sum of observations. Annals of Mathematical Statistics 23, 493–509 (1952)
Erickson, R.E., Monma, C.L., Veinott Jr., A.F.: Send-and-split method for minimum concave-cost network flows. Mathematics of Operations Research 12, 634–664 (1987)
Fleischer, L.K.: Approximating fractional multicommodity flow independent of the number of commodities. SIAM Journal on Discrete Mathematics 13, 505–520 (2000)
Garg, N., Könemann, J.: Faster and simpler algorithms for multicommodity flow and other fractional packing problems. In: Proceedings of the 39th Annual IEEE Symposium on Foundations of Computer Science, pp. 300–309 (1998)
Grigoriadis, M.D., Khachiyan, L.G.: Fast approximation schemes for convex programs with many blocks and coupling constraints. SIAM Journal on Optimization 4, 86–107 (1994)
Grigoriadis, M.D., Khachiyan, L.G.: Coordination complexity of parallel price-directive decomposition. Mathematics of Operations Research 21, 321–340 (1996)
Ho, T.-Y., Chang, Y.-W., Chen, S.-J., Lee, D.-T.: A fast crosstalkand performance-driven multilevel routing system. In: Proceedings of the IEEE International Conference on Computer-Aided Design (November 2003)
Hu, J., Sapatnekar, S.S.: A survey on multi-net global routing for intergated circuits. Integration, the VLSI Journal 31, 1–49 (2001)
Jing, T., Hong, X., Bao, H., Cai, Y., Xu, J., Cheng, C., Gu, J.: Utaco: a unified timing and congestion optimizing algorithm for standard cell global routing. In: Proceedings of the Asia and South Pacific Design Automation Conference, pp. 834–839 (2003)
Karakostas, G.: Faster approximation schemes for fractional multicommodity flow problems. In: Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 166–173 (2002)
Karp, R.M., Leighton, F.T., Rivest, R.L., Thompson, C.D., Vazirani, U.V., Vazirani, V.V.: Global wire routing in two-dimensional arrays. Algorithmica 2, 113–129 (1987)
Leighton, T., Lu, C.-J., Rao, S., Srinivasan, A.: New algorithmic aspects of the Local Lemma with applications to routing and partitioning. SIAM Journal on Computing 31, 626–641 (2001)
Müller, D.: Bestimmung der Verdrahtungskapazitäten im Global Routing von VLSI-Chips. Diploma thesis, University of Bonn (2002)
Plotkin, S.A., Shmoys, D.B., Tardos, É.: Fast approximation algorithms for fractional packing and covering problems. Mathematics of Operations Research 20, 257–301 (1995)
Raghavan, P.: Randomized rounding and discrete ham-sandwich theorems: provably good algorithms for routing and packing problems. Ph.D. thesis, Report No. UCB/CSD 87/312, University of California, Berkeley (1986)
Raghavan, P.: Probabilistic construction of deterministic algorithms: approximating packing integer programs. Journal of Computer and System Sciences 37, 130–143 (1988)
Raghavan, P., Thompson, C.D.: Randomized rounding: a technique for provably good algorithms and algorithmic proofs. Combinatorica 7, 365–374 (1987)
Raghavan, P., Thompson, C.D.: Multiterminal global routing: a deterministic approximation. Algorithmica 6, 73–82 (1991)
Roughgarden, T., Tardos, É.: How bad is selfish routing? In: Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science, pp. 93–102 (2000)
Schulz, A., Stier Moses, N.: Performance of user equilibria in traffic networks. In: Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 86–87 (2003)
Shahrokhi, F., Matula, D.W.: The maximum concurrent flow problem. Journal of the ACM 37, 318–334 (1990)
Vygen, J.: Disjoint paths. Report No. 94816–OR, Research Institute for Discrete Mathematics, University of Bonn (1994)
Xu, J., Hong, X., Jing, T., Cai, Y., Gu, J.: A novel timing-driven global routing algorithm considering coupling effects for high performance circuit design. In: Proceedings of the Asia and South Pacific Design Automation Conference, pp. 847–850 (2003)
Young, N.E.: Randomized rounding without solving the linear program. In: Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 170–178 (1995)
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Vygen, J. (2004). Near-Optimum Global Routing with Coupling, Delay Bounds, and Power Consumption. In: Bienstock, D., Nemhauser, G. (eds) Integer Programming and Combinatorial Optimization. IPCO 2004. Lecture Notes in Computer Science, vol 3064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25960-2_24
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DOI: https://doi.org/10.1007/978-3-540-25960-2_24
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