Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
Approximation algorithms for NP-complete problems on planar graphs
Journal of the ACM (JACM)
The Complexity of Multiterminal Cuts
SIAM Journal on Computing
Discrete Applied Mathematics
Journal of the ACM (JACM)
Resolvability in graphs and the metric dimension of a graph
Discrete Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Bidimensionality: new connections between FPT algorithms and PTASs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Approximation complexity of Metric Dimension problem
Journal of Discrete Algorithms
Network Discovery and Verification
IEEE Journal on Selected Areas in Communications
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
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
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The metric dimension of a graph G is the size of a smallest subset L⊆V(G) such that for any x,y∈V(G) there is a z∈L such that the graph distance between x and z differs from the graph distance between y and z. Even though this notion has been part of the literature for almost 40 years, the computational complexity of determining the metric dimension of a graph is still very unclear. Essentially, we only know the problem to be NP-hard for general graphs, to be polynomial-time solvable on trees, and to have a logn-approximation algorithm for general graphs. In this paper, we show tight complexity boundaries for the Metric Dimension problem. We achieve this by giving two complementary results. First, we show that the Metric Dimension problem on bounded-degree planar graphs is NP-complete. Then, we give a polynomial-time algorithm for determining the metric dimension of outerplanar graphs.