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Abstrakty
A set C of vertices in a graph G = (V, E) is an identifying code if it is dominating and any two vertices of V are dominated by distinct sets of codewords. This paper presents a survey of Iiro Honkala’s contributions to the study of identifying codes with respect to several aspects: complexity of computing an identifying code, combinatorics in binary Hamming spaces, infinite grids, relationships between identifying codes and usual parameters in graphs, structural properties of graphs admitting identifying codes, and number of optimal identifying codes.
Wydawca
Czasopismo
Rocznik
Tom
Strony
165--196
Opis fizyczny
Bibliogr. 85 poz., rys.
Twórcy
autor
- Télélcom Paris, France
autor
- University of Turku, Finland
autor
- CNRS, Universit´e Paris-Saclay, France
Bibliografia
- [1] Auger D. Induced paths in twin-free graphs, Electron. J. Combin. 15(1) (2008), N17. doi:10.37236/892.
- [2]* Auger D, Charon I, Honkala I, Hudry O, and Lobstein A. Edge number, minimum degree, maximum independent set, radius and diameter in twin-free graphs, Adv. Math. Commun. 3(1) (2009), 97-114. Erratum 2009. 3(4):429-430. doi:10.3934/amc.2009.3.97.
- [3] Auger D, Charon I, Hudry O, and Lobstein A. Complexity results for identifying codes in planar graphs, Int. Trans. Oper. Res. 2010. 17(6):691-710. doi:10.1111/j.1475-3995.2009.00750.x.
- [4] Ben-Haim Y, and Litsyn S. Exact minimum density of codes identifying vertices in the square grid, SIAM J. Discrete Math. 2005. 19:69-82. doi:10.1137/S089548010444408.
- [5] Bertrand N. Codes identifiants et codes localisateurs-dominateurs sur certains graphes, mémoire de stage de maîtres, ENST, Paris, France 2001, 28 pages.
- [6]* Blass U, Honkala I, and Litsyn S. On the size of identifying codes, Lecture Notes in Comput. Sci. 1999. 1719:142-147. doi:10.1007/3-540-46796-3 14.
- [7]* Blass U, Honkala I, and Litsyn S. On binary codes for identification, J. Combin. Des. 8 (2000), 151-156. https://doi.org/10.1002/(SICI)1520-6610(2000)8:2<151.
- [8]* Blass U, Honkala I, and Litsyn S. Bounds on identifying codes, Discrete Math., Selected Papers in Honor of Helge Tverberg, 2001. 241:119-128.
- [9] Charon I, Cohen G, Hudry O, and Lobstein A. New identifying codes in the binary Hamming space, European J. Combin. 2010. 31:491-501. doi:10.1016/j.ejc.2009.03.032.
- [10]* Charon I, Honkala I, Hudry O and Lobstein A. General bounds for identifying codes in some infinite regular graphs, Electron. J. Combin. 2001. 8(1):R39.
- [11]* Charon I, Honkala I, Hudry O, and Lobstein A. The minimum density of an identifying code in the king lattice, Discrete Math. 2004. 276:95-109. doi:10.1016/S0012-365X(03)00306-6.
- [12]* Charon I, Honkala I, Hudry O and Lobstein A, Structural properties of twin-free graphs, Electron. J. Combin. 2007. 14(1):R16.
- [13]* Charon I, Honkala I, Hudry O and Lobstein A, Minimum sizes of identifying codes in graphs differing by one vertex, Cryptogr. Commun. 2013. 5:119-136.
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- [20]* Cohen G, Honkala I, Lobstein A, and Zémor G. Bounds for codes identifying vertices in the hexagonal grid, SIAM J. Discrete Math. 2000. 13:492-504. doi:10.1137/S0895480199360990.
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- [33] Foucaud F. Decision and approximation complexity for identifying codes and locating-dominating sets in restricted graph classes. J. Discrete Alg. 2015. 31:48-68. doi:10.1016/j.jda.2014.08.004.
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- [40]* Honkala I. An optimal strongly identifying code in the infinite triangular grid, Electron. J. Combin. 2010. 17(1):R91. doi:10.37236/363.
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- [43]* Honkala I, Karpovsky MG, and Levitin LB. On robust and dynamic identifying codes, IEEE Trans. Inform. Theory 2006. 52: 599-612. doi:10.1109/TIT.2005.862097.
- [44]* Honkala I, and Laihonen T. On identifying codes in the triangular and square grids, SIAM J. Comput. 2004. 33:304-312. doi:10.1137/S009753970343311.
- [45]* Honkala I, and Laihonen T. On identifying codes that are robust against edge changes, Inform. and Comput. 2007. 205:1078-1095. doi:10.1016/j.ic.2007.01.003.
- [46]* Honkala I, and Laihonen T. On a new class of identifying codes in graphs, Inform. Process. Lett. 2007. 102:92-98. doi:10.1016/j.ipl.2006.11.007.
- [47]* Honkala I, and Laihonen T. On vertex-robust identifying codes of level three, Ars Combin. 2010. 94:115-127.
- [48]* Honkala I, Laihonen T, and Ranto S. On codes identifying sets of vertices in Hamming spaces, Des. Codes Cryptogr. 2001. 24:193-204. doi:10.1023/A:1011256721935.
- [49]* Honkala I, Laihonen T, and Ranto S. On strongly identifying codes, Discrete Math. 2002. 254:191-205. doi:10.1016/S0012-365X(01)00357-0.
- [50]* Honkala I, Laihonen T, and Ranto S. On locating-dominating codes in binary Hamming spaces, Discrete Math. Theor. Comput. Sci. 2004. 6:265-282. doi:10.46298/dmtcs.322.
- [51]* Honkala I, and Lobstein A. On the density of identifying codes in the square lattice, J. Combin. Theory, Ser. B 2002. 85:297-306. doi:10.1006/jctb.2001.2106.
- [52]* Honkala I, and Lobstein A. On identifying codes in binary Hamming spaces, J. Combin. Theory, Ser. A 2002.99:232-243. doi:10.1006/jcta.2002.3263.
- [53]* Honkala I, and Lobstein A, On the complexity of the identification problem in Hamming spaces, Acta Inform. 2002. 38:839-845. doi:10.1007/s00236-002-0093-4.
- [54]* Honkala I, and Lobstein A. On identification in Z2 using translates of given patterns, J. UCS 2003. 9(10):1204-1219. doi:10.3217/jucs-009-10-1204.
- [55] Hudry O, and Lobstein A. More results on the complexity of identifying problems in graphs, Theor. Comput. Sci. 2016. 626:1-12. doi:10.1016/j.tcs.2016.01.021.
- [56] Hudry O, and Lobstein A. Unique (optimal) solutions: complexity results for identifying and locating-dominating codes, Theor. Comput. Sci. 2019. 767:83-102. doi:10.1016/j.tcs.2018.09.034.
- [57] Janson S, and Laihonen T. On the size of identifying codes in binary hypercubes, J. Combin. Theory, Ser. A 2009. 116:1087-1096. doi:10.1016/j.jcta.2009.02.004.
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- [59] Junnila V. New lower bound for 2-identifying code in the square grid, Discrete Appl. Math. 2013. 161:2042-2051. doi:10.1016/j.dam.2013.02.032.
- [60] Junnila V, and Laihonen T. Identification in Z2 using Euclidean balls, Discrete Appl. Math. 2011. 159:335-343. doi:10.1016/j.dam.2010.12.008.
- [61] Junnila V, and Laihonen T. Optimal lower bound for 2-identifying codes in the hexagonal grid, Electron. J. Combin. 2012. 19(2):P38. doi:10.37236/2414.
- [62] Karpovsky MG, Chakrabarty K, and Levitin LB. On a new class of codes for identifying vertices in graphs, IEEE Trans. Inform. Theory 1998. 44:599-611.
- [63] Laihonen T. Sequences of optimal identifying codes, IEEE Trans. Inform. Theory 2002. 48:774-776. doi:10.1109/18.986043.
- [64] Laihonen T. Optimal codes for strong identification, European J. Combin. 2002. 23:307-313. doi:10.1006/eujc.2002.0571.
- [65] Laihonen T. On optimal edge-robust and vertex-robust (1, ≤ ℓ)-identifying codes, SIAM J. Discrete Math. 2005. 18(4):825-834. doi:10.1137/S0895480104440754.
- [66] Laihonen T. Optimal t-edge-robust r-identifying codes in the king lattice, Graphs Combin. 2006. 22:487-496. doi:10.1007/s00373-006-0682-z.
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- [72] Moncel J. Monotonicity of the minimum cardinality of an identifying code in the hypercube, Discrete Appl. Math. 2006. 154:898-899. doi:10.1016/j.dam.2005.05.030.
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