Implementing the L ∞  Segment Voronoi Diagram in CGAL and Applying in VLSI Pattern Analysis

  • Panagiotis Cheilaris
  • Sandeep Kumar Dey
  • Maria Gabrani
  • Evanthia Papadopoulou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8592)

Abstract

In this work we present a CGAL (Computational Geometry Algorithm Library) implementation of the line segment Voronoi diagram under the L  ∞  metric, building on top of the existing line segment Voronoi diagram under the Euclidean (L 2) metric in CGAL. CGAL is an open-source collection of geometric algorithms implemented in C++, used in both academia and industry. We also discuss an application of the L  ∞  segment Voronoi diagram in the area of VLSI pattern analysis. In particular, we identify potentially critical locations in VLSI design patterns, where a pattern, when printed, may differ substantially from the original intended VLSI design, improving on existing methods.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abdo, A., Viswanathan, R.: The feasibility of using image parameters for test pattern selection during OPC model calibration. In: Proc. SPIE, vol. 7640, p. 76401E (2010)Google Scholar
  2. 2.
    Aichholzer, O., Aurenhammer, F.: Straight skeletons for general polygonal figures in the plane. In: Cai, J.-Y., Wong, C.K. (eds.) COCOON 1996. LNCS, vol. 1090, pp. 117–126. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  3. 3.
    Aurenhammer, F., Klein, R., Lee, D.T.: Voronoi Diagrams and Delaunay Triangulations. World Scientific Publishing Company, Singapore (2013)Google Scholar
  4. 4.
    Burnikel, C., Mehlhorn, K., Schirra, S.: How to compute the Voronoi diagram of line segments: Theoretical and experimental results. In: van Leeuwen, J. (ed.) ESA 1994. LNCS, vol. 855, pp. 227–239. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  5. 5.
    Devillers, O.: The Delaunay hierarchy. International Journal of Foundations of Computer Science 13, 163–180 (2002)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Karavelas, M.: A robust and efficient implementation for the segment Voronoi diagram. In: International Symposium on Voronoi Diagrams in Science and Engineering, pp. 51–62 (2004)Google Scholar
  7. 7.
    Liotta, G., Preparata, F.P., Tamassia, R.: Robust proximity queries: An illustration of degree-driven algorithm design. SIAM Journal on Computing 28(3), 864–889 (1998)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Papadopoulou, E.: Net-aware critical area extraction for opens in VLSI circuits via higher-order Voronoi diagrams. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 30(5), 704–716 (2011)CrossRefGoogle Scholar
  9. 9.
    Papadopoulou, E., Lee, D.T.: The L  ∞  Voronoi diagram of segments and VLSI applications. International Journal of Computational Geometry and Application 11(5), 502–528 (2001)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Voronoi CAA: Voronoi Critical Area Analysis. IBM CAD Tool, Department of Electronic Design Automation, IBM Microelectronics Division, Burlington, VT, initial patents: US6178539, US6317859Google Scholar
  11. 11.
    Yap, C., Dubé, T.: The exact computation paradigm. In: Computing in Euclidean Geometry, pp. 452–492 (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Panagiotis Cheilaris
    • 1
  • Sandeep Kumar Dey
    • 1
  • Maria Gabrani
    • 2
  • Evanthia Papadopoulou
    • 1
  1. 1.Faculty of InformaticsUniversità della Svizzera ItalianaSwitzerland
  2. 2.IBM Zurich Research LaboratorySwitzerland

Personalised recommendations