Abstract
We study optimization problems for the Euclidean minimum spanning tree (MST) on imprecise data. To model imprecision, we accept a set of disjoint disks in the plane as input. From each member of the set, one point must be selected, and the MST is computed over the set of selected points. We consider both minimizing and maximizing the weight of the MST over the input. The minimum weight version of the problem is known as the minimum spanning tree with neighborhoods (\(\textsc{MSTN}\)) problem, and the maximum weight version (\(\textsc{max-MSTN}\)) has not been studied previously to our knowledge. We provide deterministic and parameterized approximation algorithms for the \(\textsc{max-MSTN}\) problem, and a parameterized algorithm for the \(\textsc{MSTN}\) problem. Additionally, we present hardness of approximation proofs for both settings.
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Dorrigiv, R. et al. (2013). On Minimum-and Maximum-Weight Minimum Spanning Trees with Neighborhoods. In: Erlebach, T., Persiano, G. (eds) Approximation and Online Algorithms. WAOA 2012. Lecture Notes in Computer Science, vol 7846. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38016-7_9
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DOI: https://doi.org/10.1007/978-3-642-38016-7_9
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