On Codes Identifying Vertices in the Two-Dimensional Square Lattice with Diagonals
IEEE Transactions on Computers
On Codes Identifying Sets of Vertices in Hamming Spaces
Designs, Codes and Cryptography
Fault-tolerant locating-dominating sets
Discrete Mathematics
Grid Coverage for Surveillance and Target Location in Distributed Sensor Networks
IEEE Transactions on Computers
Optimal codes for strong identification
European Journal of Combinatorics
Families of optimal codes for strong identification
Discrete Applied Mathematics
On the density of identifying codes in the square lattice
Journal of Combinatorial Theory Series B
On tHe Size of Identifying Codes
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
On the Identification of Vertices and Edges Using Cycles
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Codes Identifying Sets of Vertices
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Minimizing the size of an identifying or locating-dominating code in a graph is NP-hard
Theoretical Computer Science
Cycles identifying vertices and edges in binary hypercubes and 2-dimensional tori
Discrete Applied Mathematics
On identification in the triangular grid
Journal of Combinatorial Theory Series B
Identifying codes in some subgraphs of the square lattice
Theoretical Computer Science - Combinatorics of the discrete plane and tilings
Identifying and locating-dominating codes on chains and cycles
European Journal of Combinatorics
A linear algorithm for minimum 1-identifying codes in oriented trees
Discrete Applied Mathematics
European Journal of Combinatorics
On locating-dominating sets in infinite grids
European Journal of Combinatorics
Constructing codes identifying sets of vertices
Designs, Codes and Cryptography
Monotonicity of the minimum cardinality of an identifying code in the hypercube
Discrete Applied Mathematics
On graphs on n vertices having an identifying code of cardinality ⌈log2(n + 1)⇸
Discrete Applied Mathematics
On a new class of identifying codes in graphs
Information Processing Letters
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
Approximability of identifying codes and locating--dominating codes
Information Processing Letters
On identifying codes that are robust against edge changes
Information and Computation
Locating sensors in paths and cycles: The case of 2-identifying codes
European Journal of Combinatorics
On cages admitting identifying codes
European Journal of Combinatorics
Discriminating codes in (bipartite) planar graphs
European Journal of Combinatorics
Identifying codes of cycles with odd orders
European Journal of Combinatorics
New bounds on binary identifying codes
Discrete Applied Mathematics
Adaptive identification in graphs
Journal of Combinatorial Theory Series A
On r-locating-dominating sets in paths
European Journal of Combinatorics
Note: On the size of identifying codes in binary hypercubes
Journal of Combinatorial Theory Series A
New identifying codes in the binary Hamming space
European Journal of Combinatorics
An optimal result for codes identifying sets of words
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Communication: Monotonicity of the minimum cardinality of an identifying code in the hypercube
Discrete Applied Mathematics
A linear algorithm for minimum 1-identifying codes in oriented trees
Discrete Applied Mathematics
Improved bounds on identifying codes in binary Hamming spaces
European Journal of Combinatorics
Joint Monitoring and Routing in Wireless Sensor Networks Using Robust Identifying Codes
Mobile Networks and Applications
Links between discriminating and identifying codes in the binary hamming space
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Minimal identifying codes in trees and planar graphs with large girth
European Journal of Combinatorics
Expert Systems with Applications: An International Journal
Identification in Z2 using Euclidean balls
Discrete Applied Mathematics
Partial linear spaces and identifying codes
European Journal of Combinatorics
Open neighborhood locating-dominating in trees
Discrete Applied Mathematics
Extremal graphs for the identifying code problem
European Journal of Combinatorics
A novel approach for failure localization in all-optical mesh networks
IEEE/ACM Transactions on Networking (TON)
On binary linear r-identifying codes
Designs, Codes and Cryptography
Identifying codes and locating-dominating sets on paths and cycles
Discrete Applied Mathematics
Adjacent link failure localization with monitoring trails in all-optical mesh networks
IEEE/ACM Transactions on Networking (TON)
Improved Bounds for $r$-Identifying Codes of the Hex Grid
SIAM Journal on Discrete Mathematics
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
The minimum identifying code graphs
Discrete Applied Mathematics
On the size of identifying codes in triangle-free graphs
Discrete Applied Mathematics
Set graphs. I. Hereditarily finite sets and extensional acyclic orientations
Discrete Applied Mathematics
Minimum sizes of identifying codes in graphs differing by one vertex
Cryptography and Communications
Watching systems in graphs: An extension of identifying codes
Discrete Applied Mathematics
Locating and identifying codes in circulant networks
Discrete Applied Mathematics
New lower bound for 2-identifying code in the square grid
Discrete Applied Mathematics
Optimal (r,≤3) -locating-dominating codes in the infinite king grid
Discrete Applied Mathematics
New bounds on the minimum density of an identifying code for the infinite hexagonal grid
Discrete Applied Mathematics
Locally identifying coloring in bounded expansion classes of graphs
Discrete Applied Mathematics
Optimal identifying codes in the infinite 3-dimensional king grid
European Journal of Combinatorics
Identifying codes of the direct product of two cliques
European Journal of Combinatorics
Identifying path covers in graphs
Journal of Discrete Algorithms
Maximum size of a minimum watching system and the graphs achieving the bound
Discrete Applied Mathematics
Choice identification of a graph
Discrete Applied Mathematics
Sphere coverings and identifying codes
Designs, Codes and Cryptography
Minimum sizes of identifying codes in graphs differing by one edge
Cryptography and Communications
Hi-index | 754.84 |
We investigate a new class of codes for the optimal covering of vertices in an undirected graph G such that any vertex in G can be uniquely identified by examining the vertices that cover it. We define a ball of radius t centered on a vertex υ to be the set of vertices in G that are at distance at most t from υ. The vertex υ is then said to cover itself and every other vertex in the ball with center υ. Our formal problem statement is as follows: given an undirected graph G and an integer t⩾1, find a (minimal) set C of vertices such that every vertex in G belongs to a unique set of balls of radius t centered at the vertices in C. The set of vertices thus obtained constitutes a code for vertex identification. We first develop topology-independent bounds on the size of C. We then develop methods for constructing C for several specific topologies such as binary cubes, nonbinary cubes, and trees. We also describe the identification of sets of vertices using covering codes that uniquely identify single vertices. We develop methods for constructing optimal topologies that yield identifying codes with a minimum number of codewords. Finally, we describe an application of the theory developed in this paper to fault diagnosis of multiprocessor systems