SC22/WG20 N1014

From kuester@saphor.de Mon Feb 10 18:18:07 2003

From: Marc Wilhelm Kuester <kuester@saphor.de>

Subject: Sorting text

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A few ideas on sorting

Marc Wilhelm Küster

A few loose terms:

sorting: a well-defined arrangement of two sortables using the

algorithm that is specified later on

sortable: a sequence of one or more orderables. The type of a

sortable is defined by the sequence of types of the orderables

orderable: a unit which has a well-defined ordering with regards to

other units of the same type

ordering: the arrangement of two units of the same type into a

well-defined sequence

Note: A special case of ordering is string ordering

Note: Two units can be considered to be of the same type if their

respective values have a comparison function that puts them into a

well-defined greater-than relationship.

Note: In reality, sortables will be read from some datasource. This

datasource can be a structured file (e.g. an XML-based file format),

a relational database, an object-oriented database or something else

that can deliver structured data.

Sorting vs. ordering

In usual English parlance sorting and ordering are roughly

equivalent terms. For the purpose of this text they have different

meanings, however: Ordering is the arrangement of basic units such

as strings or numbers into a well-defined order whereas sorting is

the arrangement of sequences of orderable units into a well-defined

order.

An example for this distinction is the ordering of simple strings

such as abacus and abc in contrast to the sorting of phone book

entries where each entry consists of (e.g.) a family name, one or

more first names, a street name, a house number and finally a

telephone number.

The rules for sorting are culturally sensitive as well as

potentially subject to personal preferences. It is likewise

dependent on the type of sortable at hand and the field of

application.

A document on this issue must define a sample syntax for a

unambiguous definition of the sorting rules within this framework.

The multikey algorithm

Any sorting problem can be solved by a the following algorithm,

usually known as the multikey algorithm. Two sortables can be

compared by:

1. Taking the first orderable from both sortables

1a. If using "word-by-word ordering" for strings, split the

orderable along the desired split criterion (usually whitespace)

and follow this algorithm for each of the resulting parts

2. Apply any required preprocessing to each of the two orderables

3. Comparing the two resulting units. If they have a unique

ordering, than this is the sequence of the two sortables

Repeat this algorithm for all orderables until a unique sequence

could be found. If no sequence can be found, the sortables are

considered equivalent.

Preprocessing

Preprocessing of orderables is for some types of orderables a

necessity in most fields of application.

For strings, preprocessing can be seen conceptionally as the

application of UNIX-style regular expressions to a string (though in

reality, it would rarely be defined in this manner).

Preprocessing is culturally sensitive. Rules for preprocessing are

traditionally defined in national sorting standards such as NF Z

44-001 for France, DIN 5007-2 for Germany and (to a lesser extend)

ANSI/NISO Z39.75 for the US.

A sample syntax must allow for the definition of (potentially

complex) preprocessing rules.

Ordering

Each of the orderables needs a well-defined comparison method. For

some orderables such as natural numbers the ordering will rarely be

disputed and could hardly be considered to be culturally

sensitive. For other units such as strings the comparison method is

highly dependend on the culture in question (cf. ISO/IEC

14651). For yet other types such as complex numbers there is no

single accepted comparison method. Yet other types may have

monetary or other unit signs attached to them which will directly

influence the comparison (e.g. 1 cm compared to 1 inch or USD 1

compared to EUR 1).

A sample syntax must allow for the definition of ordering rules for

different types of orderables and potentially for different rules

for orderables of the same type when they appear in different

positions of the same sortable.

Syntax

The TR must provide a sample syntax for the customized specification

of an internationalized sorting algorithm much in the same vein that

ISO/IEC 14651 provides a sample syntax for defining culturally

adapted ordering specifications.

This sample syntax will be XML based (and thus also be ISO 8879

conformant). It should be able to drive an application.

Preparation of a quality document

This paper sketches the basics for an internationalized sorting

algorithm. The details for the configuration and implementation of

such an algorithm are still open. In order to get a quality

document, an open-source reference sample application should be

developed in sync with the progress of this document.

Sample application

The reference application should use object-oriented techniques

consistently to minimize the porting effort between OO-languages. C#

(ISO/IEC 23270) is suggested as a suitable language for the

reference implementation.

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Marc Wilhelm Küster

Saphor GmbH

Fronländer 22

D-72072 Tübingen

Tel.: (+49) / (0)7472 / 949 100

Fax: (+49) / (0)7472 / 949 114

E-Mail: kuester@saphor.net

Web: http://www.saphor.net