Efficient algorithms for the minimum diameter bridge problem

Authors:
Takeshi Tokuyama
Affiliations:
Graduate School of Information Sciences, Tohoku University, Sendai, 980-8579 Japan
Venue:
Computational Geometry: Theory and Applications - Special issue on Discrete and computational geometry
Year:
2003

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Abstract

We give efficient algorithms for constructing a bridge between two convex regions in a fixed dimensional space so that the diameter of the bridged region is minimized. If both the set of vertices and the set of halfspaces defining the facets of the convex regions are given, we have an optimal linear time algorithm. If only vertices are given, we give a subquadratic time algorithm, and if only halfspaces are given, we give a quadratic time algorithm.