Collation

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Collation is the assembly of written information into a standard order. Many systems of collation are based on numerical order or alphabetical order, or extensions and combinations thereof. Collating lists of words or names into alphabetical order is the basis of most office filing systems, library catalogs and reference books.

Collation differs from classification in that classification is concerned with arranging information into logical categories, while collation is concerned with the ordering of items of information, usually based on the form of their identifiers.

A collation algorithm such as the Unicode collation algorithm differs from a sorting algorithm : the first is a process to define the order, which corresponds to the process of just comparing two values, while a sorting algorithm is a procedure to put a list of items in this order.

Collation defines a total preorder on the set of possible items, typically by defining a total order on a sortkey. Note that purely numerical sorting of strings representing numbers may provide only a partial preorder on the strings, because for example 2e3 and 2000 have the same ranking, and 2 and 2.0 also. The numbers represented by the strings are totally ordered.

The main advantage of collation is that it makes it fast and easy to find an element in the list, or to confirm that it is absent from the list (for example using a binary search algorithm or interpolation search, either automatically, or – roughly and perhaps unconsciously – manually). Other advantages of numerically sorted lists are that one can easily find the first or last n elements (e.g. the 5 smallest countries or 3 largest countries), and the elements in a given range (e.g. countries with an area between .. and .. square km).

wikipedia link: Collation