论文信息 - On locating-dominating sets in infinite grids

On locating-dominating sets in infinite grids

Determining a malfunctioning component in a processor network gives the motivation for locating-dominating sets. It is shown that the smallest possible density of a locating-dominating set in the king grid equals 1/5 and in the hexagonal mesh 1/3. Moreover, we discuss a natural modification of locating-dominating sets.

Iiro S. Honkala | Tero Laihonen | I. Honkala | T. Laihonen

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

[2] Iiro S. Honkala,et al. An optimal locating-dominating set in the infinite triangular grid , 2006, Discret. Math..

[3] Iiro S. Honkala,et al. On Locating-Dominating Codes in Binary Hamming Spaces , 2004, Discret. Math. Theor. Comput. Sci..

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

[5] Mark G. Karpovsky,et al. On robust and dynamic identifying codes , 2006, IEEE Transactions on Information Theory.

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

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

[8] Antoine Lobstein,et al. Extremal cardinalities for identifying and locating-dominating codes in graphs , 2007, Discret. Math..

[9] Peter J. Slater. Domination and location in acyclic graphs , 1987, Networks.

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

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