A coloring problem in Hamming spaces
European Journal of Combinatorics
On Codes Identifying Vertices in the Two-Dimensional Square Lattice with Diagonals
IEEE Transactions on Computers
Bounds for Codes Identifying Vertices in the Hexagonal Grid
SIAM Journal on Discrete Mathematics
Fault-tolerant locating-dominating sets
Discrete Mathematics
Optimal codes for strong identification
European Journal of Combinatorics
Families of optimal codes for strong identification
Discrete Applied Mathematics
On Identifying Codes in the Triangular and Square Grids
SIAM Journal on Computing
Identifying and locating-dominating codes on chains and cycles
European Journal of Combinatorics
On Optimal Edge-Robust and Vertex-Robust $(1,\leq l)$-Identifying Codes
SIAM Journal on Discrete Mathematics
Exact Minimum Density of Codes Identifying Vertices in the Square Grid
SIAM Journal on Discrete Mathematics
On locating-dominating sets in infinite grids
European Journal of Combinatorics
Optimal t-Edge-Robust r-Identifying Codes in the King Lattice
Graphs and Combinatorics
A family of optimal identifying codes in Z2
Journal of Combinatorial Theory Series A - Special issue in honor of Jacobus H. van Lint
On robust identification in the square and king grids
Discrete Applied Mathematics
On a new class of codes for identifying vertices in graphs
IEEE Transactions on Information Theory
Sequences of optimal identifying codes
IEEE Transactions on Information Theory
On robust and dynamic identifying codes
IEEE Transactions on Information Theory
Minimum sizes of identifying codes in graphs differing by one vertex
Cryptography and Communications
Minimum sizes of identifying codes in graphs differing by one edge
Cryptography and Communications
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Assume that G=(V, E) is an undirected graph, and C@?V. For every v@?V, denote I"r(G; v)={u@?C: d(u,v)@?r}, where d(u,v) denotes the number of edges on any shortest path from u to v in G. If all the sets I"r(G; v) for v@?V are pairwise different, and none of them is the empty set, the code C is called r-identifying. The motivation for identifying codes comes, for instance, from finding faulty processors in multiprocessor systems or from location detection in emergency sensor networks. The underlying architecture is modelled by a graph. We study various types of identifying codes that are robust against six natural changes in the graph; known or unknown edge deletions, additions or both. Our focus is on the radius r=1. We show that in the infinite square grid the optimal density of a 1-identifying code that is robust against one unknown edge deletion is 1/2 and the optimal density of a 1-identifying code that is robust against one unknown edge addition equals 3/4 in the infinite hexagonal mesh. Moreover, although it is shown that all six problems are in general different, we prove that in the binary hypercube there are cases where five of the six problems coincide.