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On Two-Dimensional Via Assignment for Single-Row Routing

Published: 01 June 1988 Publication History

Abstract

The authors study the via assignment problem when vias are allowed to appear rowwise as well as columnwise. Previously they proved that the problem belongs to the class of NP-hard problems and therefore it is unlikely that polynomial-time algorithms exist for solving the problem. Two heuristics (HEU1 and HEU2) to solve the problem were proposed. HEU1 splits the nets before any routing is done while HEU2 assigns the nets alternately to via rows and via columns. Here they modify HEU2 so that the side of the board to which the nets are assigned first for connection is selected according to a desired ratio of board width to height.

References

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{1} H. So, "Some theoretical results on the routing of multi-layer printed wiring boards," in Proc. IEEE 1974 Symp, Circuits Syst., pp. 296- 303.
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{2} B. S. Ting, E. S. Kuh, and I. Shirakawa, "The multi-layer routing problem. Algorithms and necessary and sufficient conditions for the single-row single-layer case," IEEE Trans. Circuits Syst., vol. CAS- 23, pp. 768-778, Dec. 1976.
[3]
{3} B. S. Ting, E. S. Kuh, and A. Sangiovani-Vincentelly, "Via assignment problem in multi-layer printed circuit boards," IEEE Trans. Circuit Syst., vol. CAS-26, pp. 257-272, Apr. 1979.
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{4} T. F. Gonzalez, "An approximation algorithm for the multivia assignment problem," IEEE Trans. Comput.-Aided Design, vol. CAD-3, pp. 257-264, Oct. 1984.
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{5} S. Tsukiyama, I. Shirakawa, and S. Asahara, "An algorithm for the via assignment problem in backboard wiring," IEEE Trans. Circuit Syst., vol. CAS-26, pp. 369-377, June 1979.
[6]
{6} J. Bhasker and S. Sahni, "Via Assignment in single row routing," Dep. Comput. Sci. Tech. Rep. 84-19, Univ. Minnesota, Minneapolis, MN 55455, June 1984.
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{7} M. R. Garey and S. D. Johnson, Computers and Intractability. A Guide to the Theory of NP-Completeness. San Francisco, CA: Freeman, 1979.
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{8} T. J. Schaefer, "The complexity of satisfiability problems," in Proc. 10th Annu. Symp. Theory Comput., ACM, pp. 216-226.
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{9} E. L. Lawler, Combinatorial Optimization: Networks and Matroids . New York: Holt, Rinehart, and Winston, 1976.
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{10} R. Raghavan and S. Sahni, "The complexity of single row routing," Dep. Comput. Sci. Tech. Rep. 81-32, Univ. Minnesota, Minneapolis, MN 55455.
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{11} M. T. Doreau and P. Koziol, "TWIGY--A Topological algorithm based routing system," in Proc. 18th Design Automat. Conf., 1981, pp. 746-755.
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{12} J. B. Kruskal, "On the shortest spanning subtree of a graph and the traveling salesman problem," Proc. Amer. Math. Soc., vol. 7, pp. 48-50, 1956.
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{13} H. C. Du, O. H. Ibarra, and J. F. Naveda, "On two dimensional via assignment problem for single row routing," Dep. Comput. Sci. Department Tech. Rep. 85-27, Univ. Minnesota, Minneapolis, MN 55455.

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Published In

cover image IEEE Transactions on Computers
IEEE Transactions on Computers  Volume 37, Issue 6
June 1988
136 pages

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IEEE Computer Society

United States

Publication History

Published: 01 June 1988

Author Tags

  1. HEU1
  2. HEU2
  3. NP-hard problems
  4. circuit layout CAD
  5. directed graphs
  6. polynomial-time algorithms
  7. printed circuits.
  8. single-row routing
  9. two-dimensional via assignment

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