Abstract
We study a generalization of the well known bottleneck spanning tree problem called Best Case Connectivity with Uncertainty: Given a family of geometric regions, choose one point per region, such that the length of the longest edge in a spanning tree of a disc intersection graph is minimized. We show that this problem is NP-hard even for very simple scenarios such as line segments and squares. We also give exact and approximation algorithms for the case of line segments and unit discs respectively.
The authors are grateful for two Bellairs workshops supporting this research: the 8th and 9th McGill—INRIA Workshop on Computational Geometry in 2009 and 2010.
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Chambers, E. et al. (2010). Connectivity Graphs of Uncertainty Regions. In: Cheong, O., Chwa, KY., Park, K. (eds) Algorithms and Computation. ISAAC 2010. Lecture Notes in Computer Science, vol 6507. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17514-5_37
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DOI: https://doi.org/10.1007/978-3-642-17514-5_37
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