On robust and dynamic identifying codes

A subset C of vertices in an undirected graph G=(V,E) is called a 1-identifying code if the sets I(v)={u/spl isin/C:d(u,v)/spl les/1}, v/spl isin/V, are nonempty and no two of them are the same set. It is natural to consider classes of codes that retain the identification property under various conditions, e.g., when the sets I(v) are possibly slightly corrupted. We consider two such classes of robust codes. We also consider dynamic identifying codes, i.e., walks in G whose vertices form an identifying code in G.

[1]  Nathalie Bertrand,et al.  Identifying and locating-dominating codes on chains and cycles , 2004, Eur. J. Comb..

[2]  Iiro S. Honkala,et al.  On the Identification of Sets of Points in the Square Lattice , 2003, Discret. Comput. Geom..

[3]  George Cybenko,et al.  Mobile agents: the next generation in distributed computing , 1997, Proceedings of IEEE International Symposium on Parallel Algorithms Architecture Synthesis.

[4]  Antoine Lobstein,et al.  Identifying Codes with Small Radius in Some Infinite Regular Graphs , 2002, Electron. J. Comb..

[5]  Iiro S. Honkala,et al.  Codes for Identification in the King Lattice , 2003, Graphs Comb..

[6]  Tero Laihonen Optimal Codes for Strong Identification , 2002, Eur. J. Comb..

[7]  Iiro S. Honkala,et al.  On Identification in ZZ2 Using Translates of Given Patterns , 2003, J. Univers. Comput. Sci..

[8]  Gérard D. Cohen,et al.  On identifying codes , 1999, Codes and Association Schemes.

[9]  Gérard D. Cohen,et al.  Linear Codes with Covering Radius and Codimension , 2001 .

[10]  Iiro S. Honkala,et al.  On strongly identifying codes , 2002, Discret. Math..

[11]  George Cybenko,et al.  D'Agents: Applications and performance of a mobile‐agent system , 2002, Softw. Pract. Exp..

[12]  Tero Laihonen,et al.  Sequences of optimal identifying codes , 2002, IEEE Trans. Inf. Theory.

[13]  Antoine Lobstein,et al.  Minimizing the size of an identifying or locating-dominating code in a graph is NP-hard , 2003, Theor. Comput. Sci..

[14]  Iiro Honkala,et al.  An Optimal Edge-Robust Identifying Code in the Triangular Lattice , 2004 .

[15]  Tero Laihonen,et al.  Codes Identifying Sets of Vertices , 2001, AAECC.

[16]  Iiro S. Honkala,et al.  On Codes Identifying Sets of Vertices in Hamming Spaces , 2000, Des. Codes Cryptogr..

[17]  Iiro S. Honkala,et al.  The minimum density of an identifying code in the king lattice , 2004, Discret. Math..

[18]  Iiro S. Honkala,et al.  General Bounds for Identifying Codes in Some Infinite Regular Graphs , 2001, Electron. J. Comb..

[19]  Peter J. Slater,et al.  Fundamentals of domination in graphs , 1998, Pure and applied mathematics.

[20]  Simon Litsyn,et al.  Bounds on identifying codes , 2001, Discret. Math..

[21]  Mark G. Karpovsky,et al.  On a New Class of Codes for Identifying Vertices in Graphs , 1998, IEEE Trans. Inf. Theory.

[22]  Gérard D. Cohen,et al.  New Bounds for Codes Identifying Vertices in Graphs , 1999, Electron. J. Comb..

[23]  Francesco De Pellegrini,et al.  Robust location detection in emergency sensor networks , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[24]  Tero Laihonen,et al.  Families of optimal codes for strong identification , 2002, Discret. Appl. Math..

[25]  Axthonv G. Oettinger,et al.  IEEE Transactions on Information Theory , 1998 .

[26]  O. Antoine,et al.  Theory of Error-correcting Codes , 2022 .

[27]  Peter J. Slater,et al.  Fault-tolerant locating-dominating sets , 2002, Discret. Math..

[28]  Simon Litsyn,et al.  Exact Minimum Density of Codes Identifying Vertices in the Square Grid , 2005, SIAM J. Discret. Math..

[29]  Sanna M. Ranto Optimal linear identifying codes , 2003, IEEE Trans. Inf. Theory.

[30]  George Cybenko,et al.  D'Agents: Security in a Multiple-Language, Mobile-Agent System , 1998, Mobile Agents and Security.

[31]  Antoine Lobstein,et al.  Identifying and locating-dominating codes: NP-Completeness results for directed graphs , 2002, IEEE Trans. Inf. Theory.

[32]  Nathalie Bertrand,et al.  1-identifying Codes on Trees , 2005, Australas. J Comb..

[33]  Michel Mollard,et al.  On paths and cycles dominating hypercubes , 2003, Discret. Math..

[34]  Gérard D. Cohen,et al.  Covering Codes , 2005, North-Holland mathematical library.

[35]  Gérard D. Cohen,et al.  Bounds for Codes Identifying Vertices in the Hexagonal Grid , 2000, SIAM J. Discret. Math..

[36]  Iiro S. Honkala,et al.  Two families of optimal identifying codes in binary Hamming spaces , 2002, IEEE Trans. Inf. Theory.

[37]  S. Litsyn,et al.  On binary codes for identification , 2000 .

[38]  Gérard D. Cohen,et al.  On Codes Identifying Vertices in the Two-Dimensional Square Lattice with Diagonals , 2001, IEEE Trans. Computers.

[39]  IIRO HONKALA,et al.  On identifying codes in the triangular and square grids , 2004, SIAM J. Comput..

[40]  Iiro S. Honkala,et al.  On the complexity of the identification problem in Hamming spaces , 2002, Acta Informatica.

[41]  Iiro S. Honkala,et al.  On Identifying Codes in Binary Hamming Spaces , 2002, J. Comb. Theory, Ser. A.

[42]  Simon Litsyn,et al.  Short Dominating Paths and Cycles in the Binary Hypercube , 2001 .

[43]  Iiro S. Honkala,et al.  On the Density of Identifying Codes in the Square Lattice , 2002, J. Comb. Theory, Ser. B.

[44]  Iiro S. Honkala,et al.  On identifying codes in the hexagonal mesh , 2004, Inf. Process. Lett..