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The LEDA platform for combinatorial and geometric computing

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1256))

Abstract

We give an overview of the LEDA platform for combinatorial and geometric computing and an account of its development. We discuss our motivation for building LEDA and to what extent we have reached our goals. We also discuss some recent theoretical developments. This paper contains no new technical material. It is intended as a guide to existing publications about the system. We refer the reader also to our web-pages for more information.

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References

  1. A.V. Aho, J.E. Hopcroft, and J.D. Ullman. Data structures and algorithms. Addison-Wesley, 1983.

    Google Scholar 

  2. M. Blum and S. Kannan. Programs That Check Their Work. In Proc. of the 21th Annual ACM Symp. on Theory of Computing, 1989.

    Google Scholar 

  3. M. Blum, M. Luby, and R. Rubinfeld. Self-testing/correcting with applications to numerical problems. In Proc. 22nd Annual ACM Symp. on Theory of Computing, pages 73–83, 1990.

    Google Scholar 

  4. Ch. Burnikel, K. Mehlhorn, and S. Schirra. On degeneracy in geometric computations. In Proc. SODA 94, pages 16–23, 1994.

    Google Scholar 

  5. Ch. Burnikel, K. Mehlhorn, and St. Schirra. How to compute the Voronoi diagram of line segments: Theoretical and experimental results. In Springer-Verlag Berlin/New York, editor, LNCS, volume 855 of Proceedings of ESA '94, pages 227–239, 1994.

    Google Scholar 

  6. Ch. Burnikel, R.Fleischer, K. Mehlhorn, and S. Schirra. A strong and easily computable separation bound for arithmetic expressions involving square roots. In Proc. SODA 97, pages 702–709, 1997.

    Google Scholar 

  7. T.H. Cormen, C.E. Leiserson, and R.L. Rivest. Introduction to Algorithms. MIT Press/McGraw-Hill Book Company, 1990.

    Google Scholar 

  8. A. Fabri, G.-J. Giezeman, L. Kettner, S. Schirra, and S. Schönherr. The CGAL Kernel: A basis for geometric computation. In Workshop on Applied Computational Geometry (WACG96), LNCS, 1996.

    Google Scholar 

  9. Ulrich Finkler and Kurt Mehlhorn. Runtime prediction of real programs on real machines. In Proceedings 8th ACM-SIAM Symposium on Discrete Algorithms (SODA'97), January 1997.

    Google Scholar 

  10. C. Hundack, K. Mehlhorn, and S. Näher. A Simple Linear Time Algorithm for Identifying Kuratowski Subgraphs of Non-Planar Graphs. Manuscript, 1996.

    Google Scholar 

  11. J.H. Kingston. Algorithms and Data Structures. Addison-Wesley Publishing Company, 1990.

    Google Scholar 

  12. K. Mehlhorn. Data structures and algorithms 1,2, and 3. Springer, 1984.

    Google Scholar 

  13. K. Mehlhorn and P. Mutzel. On the Embedding Phase of the Hopcroft and Tarjan Planarity Testing Algorithm. Algorithmica, 16(2):233–242, 1995.

    Article  Google Scholar 

  14. K. Mehlhorn, Müller, S. Näher, S. Schirra, M. Seel, C. Uhrig, and J. Ziegler. A computational basis for higher-dimensional computational geometry and its applications. In Proceedings of the Symp. on Computational Geometry, 1997. http://www.mpi-sb.mpg.de/∼seel.

    Google Scholar 

  15. K. Mehlhorn and S. Näher. The LED A Platform for Combinatorial and Geometric Computing. Cambridge University Press, forthcoming. Draft versions of some chapters are available at http://www.mpi-sb.mpg.de/∼mehlhorn.

    Google Scholar 

  16. K. Mehlhorn and S. Näher. The implementation of geometric algorithms.In 13th World Computer Congress IFIP94, volume 1, pages 223–231. Elsevier Science B.V. North-Holland, Amsterdam, 1994.

    Google Scholar 

  17. K. Mehlhorn and S. Näher. LEDA: A platform for combinatorial and geometric computing. Communications of the ACM, 38(1):96–102, 1995.

    Article  Google Scholar 

  18. K. Mehlhorn, S. Näher, T. Schilz, S. Schirra, M. Seel, R. Seidel, and Ch. Uhrig. Checking Geometric Programs or Verification of Geometric Structures. In Proc. of the 12th Annual Symposium on Computational Geometry, pages 159–165, 1996.

    Google Scholar 

  19. Kurt Mehlhorn, S. Näher, and Ch. Uhrig. The LEDA User Manual (Version R 3.4). Technical report, Max-Planck-Institut für Informatik, 1996. http://www.mpi-sb.mpg.de/LEDA/leda.html.

    Google Scholar 

  20. J. Nievergelt and K.H. Hinrichs. Algorithms and Data Structures. Prentice Hall Inc., 1993.

    Google Scholar 

  21. J. O'Rourke. Computational Geometry in C. Cambridge University Press, 1994.

    Google Scholar 

  22. R. Sedgewick. Algorithms. Addison-Wesley Publishing Company, 1991.

    Google Scholar 

  23. Michael Seel. Eine Implementierung abstrakter Voronoidiagramme. Master's thesis, Max-Planck-Institut für Informatik, 1994.

    Google Scholar 

  24. R.E. Tarjan. Data structures and network algorithms. In CBMS-NSF Regional Conference Series in Applied Mathematics, volume 44, 1983.

    Google Scholar 

  25. C.J. van Wyk. Data Structures and C programs. Addison-Wesley Publishing Company, 1988.

    Google Scholar 

  26. D. Wood. Data Structures, Algorithms, and Performance. Addison-Wesley Publishing Company, 1993.

    Google Scholar 

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Pierpaolo Degano Roberto Gorrieri Alberto Marchetti-Spaccamela

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© 1997 Springer-Verlag Berlin Heidelberg

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Mehlhorn, K., Näher, S., Uhrig, C. (1997). The LEDA platform for combinatorial and geometric computing. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds) Automata, Languages and Programming. ICALP 1997. Lecture Notes in Computer Science, vol 1256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63165-8_161

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  • DOI: https://doi.org/10.1007/3-540-63165-8_161

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63165-1

  • Online ISBN: 978-3-540-69194-5

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