Skip to main content
Log in

Optimal t-Edge-Robust r-Identifying Codes in the King Lattice

  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract

Locating faulty processors in a multiprocessor system gives a motivation for identifying codes. The concept of a t-edge-robust r-identifying code was introduced in [8]. We consider these codes in the king lattice and give several optimal densities.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Blass, U., Honkala, I., Litsyn, S.: Bounds on identifying codes. Discrete Math. 241, 119–128 (2001)

    Google Scholar 

  2. Charon, I., Honkala, I., Hudry, O., Lobstein, A.: General bounds for identifying codes in some infinite regular graphs. Electron. J. Combin. 8 R39, (2001)

  3. Charon, I., Honkala, I., Hudry, O., Lobstein, A.: The minimum density of an identifying code in the king lattice. Discrete Math. 276, 95–109 (2004)

    Google Scholar 

  4. Charon, I., Hudry, O., Lobstein, A.: Identifying codes with small radius in some infinite regular graphs. Electron. J. Combin. 9, R11 (2002)

  5. Cohen, G., Honkala, I., Lobstein, A., Zémor, G.: Bounds for codes identifying vertices in the hexagonal grid. SIAM J. Discrete Math. 13, 492–504 (2000)

    Google Scholar 

  6. Cohen, G., Honkala, I., Lobstein, A., Zémor, G.: On codes identifying vertices in the two-dimensional square lattice with diagonals. IEEE Trans. on Computers 50, 174–176 (2001)

    Google Scholar 

  7. Honkala, I.: An optimal edge-robust identifying code in the triangular lattice, Ann. Comb. 8, 303–323 (2004)

    Google Scholar 

  8. Honkala, I., Karpovsky, M., Levitin, L.: On robust and dynamic identifying codes, IEEE Trans. Inform. Theory, to appear

  9. Honkala, I., Laihonen, T.: On the identification of sets of points in the square lattice. Discrete Comput. Geom. 29, 139–152 (2003)

    Google Scholar 

  10. Honkala, I., Laihonen, T.: On a new class of identifying codes in graphs, submitted.

  11. Karpovsky, M., Chakrabarty, K., Levitin, L.: On a new class of codes for identifying vertices in graphs. IEEE Trans. Inform. Theory 44, 599–611 (1998)

    Google Scholar 

  12. Laihonen, T.: Sequences of optimal identifying codes. IEEE Trans. Inform. Theory 48, 774–776 (2002)

    Google Scholar 

  13. Ray, S., Ungrangsi, R., De Pellegrini, F., Trachtenberg, A., Starobinski, D.: Robust location detection in emergency sensor networks. In: Proc. INFOCOM 2003, San Fancisco, March 2003

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tero Laihonen.

Additional information

Research supported by the Academy of Finland under grants 207303 and 111940.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Laihonen, T. Optimal t-Edge-Robust r-Identifying Codes in the King Lattice. Graphs and Combinatorics 22, 487–496 (2006). https://doi.org/10.1007/s00373-006-0682-z

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00373-006-0682-z

Keywords

Navigation