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Rectangles are used to approximate objects, or sets of objects, in a plethoraof applications, systems and index structures. Many tasks, such as nearestneighbor search and similarity ranking, require to decide if objects in onerectangle A may, must, or must not be closer to objects in a second rectangleB, than objects in a third rectangle R. To decide this relation of "SpatialDomination" it can be shown that using minimum and maximum distances it isoften impossible to detect spatial domination. This spatial gem provides anecessary and sufficient decision criterion for spatial domination that can becomputed efficiently even in higher dimensional space. In addition, thisspatial gem provides an example, pseudocode and an implementation in Python.

Complete and Sufficient Spatial Domination of Multidimensional Rectangles