Connectivity Graphs of Uncertainty Regions

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.

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