Skip to main content

C++ Tools for Exploiting Polyhedral Symmetries

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 6327)

Abstract

We report on the recently developed C++ tools PermLib and SymPol that are designed to support high performance work with symmetric polyhedra. The callable library PermLib provides basic support for permutation group algorithms and data structures. It can in particular be used for the development of optimization algorithms that combine methods from polyhedral combinatorics and computational group theory. The software SymPol is such an application helping to detect polyhedral symmetries and to analyze faces of polyhedra up to symmetries. It in particular provides successfully used decomposition methods for polyhedral representation conversions up to symmetries.

Keywords

  • polyhedral combinatorics
  • symmetries
  • permutation group algorithms
  • representation conversion

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bremner, D., Dutour Sikirić, M., Schürmann, A.: Polyhedral representation conversion up to symmetries. In: Bremner, D., Avis, D., Deza, A. (eds.) Proceedings of the 2006 CRM Workshop on Polyhedral Computation. CRM Proceedings & Lecture Notes, vol. 48, pp. 45–71. AMS, Providence (2009)

    Google Scholar 

  2. Dutour Sikirić, M., Schürmann, A., Vallentin, F.: Classification of eight dimensional perfect forms. Electron. Res. Announc. Amer. Math. Soc. 13, 21–32 (2007)

    CrossRef  MATH  MathSciNet  Google Scholar 

  3. Dutour Sikirić, M., Schürmann, A., Vallentin, F.: The contact polytope of the Leech lattice. Discrete Comput. Geom. (to appear), preprint at arXiv:0906.1427

    Google Scholar 

  4. Holt, D.F., Eick, B., O’Brien, E.A.: Handbook of computational group theory. Chapman & Hall/CRC, Boca Raton (2005)

    CrossRef  MATH  Google Scholar 

  5. Kumar, A.: Elliptic fibrations on a generic Jacobian Kummer surface (in preparation)

    Google Scholar 

  6. Leon, J.S.: Permutation group algorithms based on partitions. I. Theory and algorithms. J. Symbolic Comput. 12, 533–583 (1991)

    CrossRef  MATH  MathSciNet  Google Scholar 

  7. Margot, F.: Symmetry in integer linear programming. In: Jünger, M., Liebling, T.M., Naddef, D., Nemhauser, G.L., Pulleyblank, W.R., Reinelt, G., Rinaldi, G., Wolsey, L.A. (eds.) 50 Years of Integer Programming 1958–2008. Springer, Heidelberg (2009)

    Google Scholar 

  8. Rehn, T.: Fundamental Permutation Group Algorithms for Symmetry Computation, Diploma thesis (computer science), Otto von Guericke University Magdeburg (2010), http://fma2.math.uni-magdeburg.de/~latgeo/permlib/diploma-thesis-cs-rehn.pdf

  9. Santos, F.: A counterexample to the Hirsch conjecture, preprint at arxiv:1006.2814

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Rehn, T., Schürmann, A. (2010). C++ Tools for Exploiting Polyhedral Symmetries. In: Fukuda, K., Hoeven, J.v.d., Joswig, M., Takayama, N. (eds) Mathematical Software – ICMS 2010. ICMS 2010. Lecture Notes in Computer Science, vol 6327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15582-6_48

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-15582-6_48

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15581-9

  • Online ISBN: 978-3-642-15582-6

  • eBook Packages: Computer ScienceComputer Science (R0)