The Maximum Disjoint Routing Problem

  • Farhad Shahmohammadi
  • Amir Sharif-Zadeh
  • Hamid Zarrabi-Zadeh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9797)

Abstract

Motivated by the bus escape routing problem in printed circuit boards, we revisit the following problem: given a set of n axis-parallel rectangles inside a rectangular region \({\mathscr {R}}\), find the maximum number of rectangles that can be extended toward the boundary of \({\mathscr {R}}\), without overlapping each other. We provide an efficient algorithm for solving this problem in \(O(n^2 \log ^3 n \log \log n)\) time, improving over the current best \(O(n^3)\)-time algorithm available for the problem.

References

  1. 1.
    Ahmadinejad, A., Zarrabi-Zadeh, H.: The maximum disjoint set of boundary rectangles. In: Proceedings of the 26th Canadian Conference on Computational Geometry, pp. 302–307 (2014)Google Scholar
  2. 2.
    Assadi, S., Emamjomeh-Zadeh, E., Yazdanbod, S., Zarrabi-Zadeh, H.: On the rectangle escape problem. In: Proceedings of the 25th Canadian Conference on Computational Geometry, pp. 235–240 (2013)Google Scholar
  3. 3.
    Chan, W.-T., Chin, F.Y.: Efficient algorithms for finding the maximum number of disjoint paths in grids. J. Algorithms 34(2), 337–369 (2000)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Chan, W.-T., Chin, F.Y., Ting, H.-F.: A faster algorithm for finding disjoint paths in grids. In: Proceedings of the 10th International Symposium on Algorithms and Computation, pp. 393–402 (1999)Google Scholar
  5. 5.
    Fang, J.-W., Lin, I.-J., Chang, Y.-W., Wang, J.-H.: A network-flow-based RDL routing algorithm for flip-chip design. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 26(8), 1417–1429 (2007)CrossRefGoogle Scholar
  6. 6.
    Hershberger, J., Suri, S.: Efficient breakout routing in printed circuit boards. In: Proceedings of the 7th Workshop on Algorithms and Data Structures, pp. 462–471 (1997)Google Scholar
  7. 7.
    Keil, J.M., Mitchell, J.S., Pradhan, D., Vatshelle, M.: An algorithm for the maximum weight independent set problem on outerstring graphs. In: Proceedings of the 27th Canadian Conference on Computational Geometry, pp. 2–7 (2015)Google Scholar
  8. 8.
    Kong, H., Ma, Q., Yan, T., Wong, M.D.F.: An optimal algorithm for finding disjoint rectangles and its application to PCB routing. In: Proceedings of the 47th ACM/EDAC/IEEE Design Automation Conference, pp. 212–217 (2010)Google Scholar
  9. 9.
    Kong, H., Yan, T., Wong, M.D.F., Ozdal, M.M.: Optimal bus sequencing for escape routing in dense PCBs. In: Proceedings of the 2007 IEEE/ACM International Conference on Computer-Aided Design, pp. 390–395 (2007)Google Scholar
  10. 10.
    Ma, Q., Wong, M.D.F.: NP-completeness and an approximation algorithm for rectangle escape problem with application to PCB routing. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 31(9), 1356–1365 (2012)CrossRefGoogle Scholar
  11. 11.
    Ma, Q., Young, E., Wong, M.D.F.: An optimal algorithm for layer assignment of bus escape routing on PCBs. In: Proceedings of the 48th ACM/EDAC/IEEE Design Automation Conference, pp. 176–181 (2011)Google Scholar
  12. 12.
    Mehlhorn, K., Näher, S.: Dynamic fractional cascading. Algorithmica 5(1–4), 215–241 (1990)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Wu, P.-C., Ma, Q., Wong, M.D.: An ILP-based automatic bus planner for dense PCBs. In: Proceedings of the 18th Asia South Pacific Design Automation Conference, pp. 181–186 (2013)Google Scholar
  14. 14.
    Yan, T., Wong, M.D.: A correct network flow model for escape routing. In: Proceedings of the 46th ACM/EDAC/IEEE Design Automation Conference, pp. 332–335 (2009)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Farhad Shahmohammadi
    • 1
    • 2
  • Amir Sharif-Zadeh
    • 1
  • Hamid Zarrabi-Zadeh
    • 1
  1. 1.Department of Computer EngineeringSharif University of TechnologyTehranIran
  2. 2.Department of Computer ScienceUniversity of CaliforniaLos AngelesUSA

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