Definition
A region algebra is a collection of operators, each of which returns a set of regions as a result and takes as arguments one or more sets of regions. A region of a string is a pair of natural number positions (s, e) that correspond to the substring starting at s and ending at e. A position is a count of bytes, characters, or words from the beginning of the string.
Choosing a set of operators defines a particular region algebra. Operators are chosen for efficiency as well as utility. For example, if regions correspond to structure elements such as chapters and sections in a document, then many operators for querying structure conditions are useful and can be implemented efficiently. One example of such an operator is containedIn(X,Y) which takes two sets of regions X and Y and returns the subset of regions in X that are contained in some region of Y, i.e., {(sx, ex)∈X∣∃(sy, ey)∈Y(sx ≥ sy) ∧ (ex ≤ ey)}. A similar operator is contains(X,Y) which returns the subset of regions...
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Young-Lai, M. (2018). Region Algebra. In: Liu, L., Özsu, M.T. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8265-9_304
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