Abstract
Given a data structure and an ordering on the objects it contains, we study methods for obtaining a modified data structure that allows for splits and concatenations with respect to that ordering. A general technique will be given, which works for all data structures for decomposable searching problems and order decomposable set problems. Furthermore, the results imply a new method for adding range restrictions to data structures. Applications include, e.g., a version of an interval tree that allows for splitting and concatenating on the length of the intervals, a version of the d -dimensional k-d tree that allows for splitting and concatenating on all coordinates, and a data structure on points in the plane that allows for reporting the convex hull of the points in a given query rectangle.
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