The complexity of minimizing wire lengths in VLSI layouts
Information Processing Letters
Discrete Mathematics - Topics on domination
Approximating the tree and tour covers of a graph
Information Processing Letters
Upper bounds to the clique width of graphs
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
Polynomial Instances of the Positive Semidefinite and Euclidean Distance Matrix Completion Problems
SIAM Journal on Matrix Analysis and Applications
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Connected rigidity matroids and unique realizations of graphs
Journal of Combinatorial Theory Series B
A Theory of Network Localization
IEEE Transactions on Mobile Computing
Wireless Sensor Networks: Technology, Protocols, and Applications
Wireless Sensor Networks: Technology, Protocols, and Applications
Parameterized Complexity of Vertex Cover Variants
Theory of Computing Systems
Information Processing Letters
Fundamentals of Wireless Sensor Networks: Theory and Practice
Fundamentals of Wireless Sensor Networks: Theory and Practice
Parameterized Complexity
Width Parameters Beyond Tree-width and their Applications
The Computer Journal
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Network localization is important for networks with no prefixed positions of network nodes such as sensor networks. We are given a subset of the set of $\binom{n}{2}$ pairwise distances among n sensors in some Euclidean space. We want to determine the positions of each sensors from the (partial) distance information. The input can be seen as an edge weighted graph. In this paper, we present some efficient algorithms that solve this problem using the structures of input graphs, which we call the cores of them. For instance, we present a polynomial-time algorithm solving the network localization problem for graphs with connected dominating sets of bounded size. This algorithm allows us to have an FPT algorithm for some restricted instances such as graphs with connected vertex covers of bounded size.