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Given two hyper-rectangles in E with sides having surface normals in the directions of the axes, and given a connected set in each that touches all 2 n sides of its containing hyper-rectangle, it is important to have an easily calculated upper bound on the distance between the two connected sets. A result giving such a bound, necessary in branch and bound algorithms used for collision avoidance in robotic simulation, is stated and proved here. [ABSTRACT FROM AUTHOR]

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