The strong metric dimension of graphs and digraphs
Discrete Applied Mathematics
Computing minimal doubly resolving sets of graphs
Computers and Operations Research
On approximation complexity of metric dimension problem
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
network discovery and verification
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
Approximation complexity of Metric Dimension problem
Journal of Discrete Algorithms
On the metric dimension of infinite graphs
Discrete Applied Mathematics
Approximate discovery of random graphs
SAGA'07 Proceedings of the 4th international conference on Stochastic Algorithms: foundations and applications
The (weighted) metric dimension of graphs: hard and easy cases
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Resolving sets for Johnson and Kneser graphs
European Journal of Combinatorics
On the metric dimension of line graphs
Discrete Applied Mathematics
On the strong metric dimension of corona product graphs and join graphs
Discrete Applied Mathematics
Metric dimension of some distance-regular graphs
Journal of Combinatorial Optimization
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We study generators of metric spaces--sets of points with the property that every point of the space is uniquely determined by the distances from their elements. Such generators put a light on seemingly different kinds of problems in combinatorics that are not directly related to metric spaces. The two applications we present concern combinatorial search: problems on false coins known from the borderline of extremal combinatorics and information theory; and a problem known from combinatorial optimization--connected joins in graphs.We use results on the detection of false coins to approximate the metric dimension (minimum size of a generator for the metric space defined by the distances) of some particular graphs for which the problem was known and open. In the opposite direction, using metric generators, we show that the existence of connected joins in graphs can be solved in polynomial time, a problem asked in a survey paper of Frank. On the negative side we prove that the minimization of the number of components of a join is NP-hard.We further explore the metric dimension with some problems. The main problem we are led to is how to extend an isometry given on a metric generator of a metric space.