Open Access
Issue |
RAIRO-Oper. Res.
Volume 58, Number 2, March-April 2024
|
|
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Page(s) | 1633 - 1651 | |
DOI | https://doi.org/10.1051/ro/2024046 | |
Published online | 12 April 2024 |
- Y. Ben-Haim and S. Litsyn, Exact minimum density of codes identifying vertices in the square grid. SIAM J. Discrete Math. 19 (2005) 69–82. [CrossRef] [MathSciNet] [Google Scholar]
- M. Bouznif, F. Havet and M. Preissmann, Minimum-density identifying codes in square grids. Lecture Notes Comput. Sci. 11 (2016) 77–88. [CrossRef] [Google Scholar]
- I. Charon, I. Honkala, O. Hudry and A. Lobstein, General bounds for identifying codes in some infinite regular graphs. Electron. J. Comb. 8 (2001) 21. [CrossRef] [Google Scholar]
- I. Charon, O. Hudry and A. Lobstein, Identifying codes with small radius in some infinite regular graphs. Electron. J. Comb. 9 (2002) 25. [CrossRef] [Google Scholar]
- I. Charon, I. Honkala, O. Hudry and A. Lobstein, The minimum density of an identifying code in the king lattice. Discrete Math. 276 (2004) 95–109. [CrossRef] [MathSciNet] [Google Scholar]
- G.D. Cohen, I. Honkala, A. Lobstein and G. Zémor, Bounds for codes identifying vertices in the hexagonal grid. SIAM J. Discrete Math. 13 (2000) 492–504. [CrossRef] [MathSciNet] [Google Scholar]
- G.D. Cohen, I. Honkala, A. Lobstein and G. Zémor, On identifying codes, in Codes and Association Schemes (Piscataway, NJ, 1999). DIMACS Ser. Discrete Math. Theoret. Comput. Sci. Vol. 56. Amer. Math. Soc., Providence, RI (2001) 97–109. [Google Scholar]
- D.W. Cranston and D.B. West, An introduction to the discharging method via graph coloring. Discrete Math. 340 (2017) 766–793. [CrossRef] [MathSciNet] [Google Scholar]
- D.W. Cranston and G. Yu, A new lower bound on the density of vertex identifying codes for the infinite hexagonal grid. Electron. J. Comb. 16 (2009) 16. [Google Scholar]
- A. Cukierman and G. Yu, New bounds on the minimum density of an identifying code for the infinite hexagonal grid. Discrete Appl. Math. 161 (2013) 2910–2924. [CrossRef] [MathSciNet] [Google Scholar]
- M. Daniel, S. Gravier and J. Moncel, Identifying codes in some subgraphs of the square lattice. Theor. Comput. Sci. 319 (2004) 411–421. [CrossRef] [Google Scholar]
- R. Dantas, F. Havet and R.M. Sampaio, Identifying codes for infinite triangular grids with a finite number of rows. Discrete Math. 340 (2017) 1584–1597. [CrossRef] [MathSciNet] [Google Scholar]
- R. Dantas, F. Havet and R.M. Sampaio, Minimum density of identifying codes of king grids. Discrete Math. 341 (2018) 2708–2719. [CrossRef] [MathSciNet] [Google Scholar]
- F. Foucaud, Combinatorial and algorithmic aspects of identifying codes in graphs. Ph.D. thesis, Université Sciences et Technologies (2012). [Google Scholar]
- M. Hartmann and J.B. Orlin, Finding minimum cost to time ratio cycles with small integral transit times. Networks 23 (1993) 567–574. [CrossRef] [MathSciNet] [Google Scholar]
- I. Honkala and T. Laihonen, Codes for identification in the king lattice. Graphs Comb. 19 (2003) 505–516. [Google Scholar]
- I. Honkala and T. Laihonen, On the identification of sets of points in the square lattice. Discrete Comput. Geom. 29 (2003) 139–152. [Google Scholar]
- I. Honkala and T. Laihonen, On identification in the triangular grid. J. Comb. Theory Ser. B 91 (2004) 67–86. [CrossRef] [Google Scholar]
- I. Honkala and T. Laihonen, On identifying codes in the hexagonal mesh. Inf. Process. Lett. 89 (2004) 9–14. [CrossRef] [Google Scholar]
- I. Honkala and T. Laihonen, On identifying codes in the triangular and square grids. SIAM J. Comput. 33 (2004) 304–312. [CrossRef] [MathSciNet] [Google Scholar]
- I. Honkala and A. Lobstein, On the density of identifying codes in the square lattice. J. Comb. Theory Ser. B 85 (2002) 297–306. [CrossRef] [Google Scholar]
- D. Jean, Watching systems, identifying, locating-dominating and discriminating codes in graphs. Accessed on July 2023 https://dragazo.github.io/bibdom/main.pdf (2023). [Google Scholar]
- D. Jean and S. Seo, Fault-tolerant locating-dominating sets with error-correction, Preprint arXiv:2212.08193v1 (2022). [Google Scholar]
- M. Jiang, Periodicity of identifying codes in strips. Inf. Process. Lett. 135 (2018) 77–84. [CrossRef] [Google Scholar]
- V. Junnila and T. Laihonen, Optimal lower bound for 2-identifying codes in the hexagonal grid. Electron. J. Comb. 19 (2012) 16. [Google Scholar]
- R.M. Karp, A characterization of the minimum cycle mean in a digraph. Discrete Math. 23 (1978) 309–311. [CrossRef] [MathSciNet] [Google Scholar]
- M.G. Karpovsky, K. Chakrabarty and L.B. Levitin, On a new class of codes for identifying vertices in graphs. IEEE Trans. Inf. Theory 44 (1998) 599–611. [CrossRef] [Google Scholar]
- R. Martin and B. Stanton, Lower bounds for identifying codes in some infinite grids. Electron. J. Comb. 17 (2010) 16. [Google Scholar]
- V. Salo and I. Törm¨a, Finding codes on infinite grids automatically. Preprint arXiv.2303.00557 (2023). [Google Scholar]
- R. Sampaio, G. Sobral and Y. Wakabayashi, Minimum density of identifying codes of hexagonal grids with a finite number of rows, in Anais do VII Encontro de Teoria da Computação (Porto Alegre, RS, Brasil). SBC (2022) 145–148. [Google Scholar]
- P.J. Slater, Fault-tolerant locating-dominating sets. Discrete Math. 249 (2002) 179–189. [CrossRef] [MathSciNet] [Google Scholar]
- G. Sobral, R. Sampaio and Y. Wakabayashi, Identifying codes. https://gitlab.uspdigital.usp.br/gagsobral/identifying-codes (2023). [Google Scholar]
- D. Stolee, Automated discharging arguments for density problems in grids. Preprint arXiv.1409.5922 (2014). [Google Scholar]
- Z. Xiao and B. Baas, A hexagonal processor and interconnect topology for many-core architecture with dense on-chip networks, in VLSI-SoC: From Algorithms to Circuits and System-on-Chip Design. Springer Berlin Heidelberg (2013) 125–143. [Google Scholar]
- J. Zerovnik and I. Sau, An optimal permutation routing algorithm on full-duplex hexagonal networks. Discrete Math. Theor. Comput. Sci. 10 (2008) 1–15. [MathSciNet] [Google Scholar]
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