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 Brief explanation of the hyphenation algorithm herein.[1]

 Raph Levien <raph@acm.org>

 4 Aug 1998

    The hyphenation algorithm is basically the same as Knuth's TeX

 algorithm. However, the implementation is quite a bit faster.

    The hyphenation files from TeX can almost be used directly. There

 is a preprocessing step, however. If you don't do the preprocessing

 step, you'll get bad hyphenations (i.e. a silent failure).

    Start with a file such as hyphen.us. This is the TeX ushyph1.tex

 file, with the exception dictionary encoded using the same rules as

 the main portion of the file. Any line beginning with % is a comment.

 Each other line should contain exactly one rule.

    Then, do the preprocessing - "perl substrings.pl hyphen.us". The

 resulting file is hyphen.mashed. It's in Perl, and it's fairly slow

 (it uses brute force algorithms; about 17 seconds on a P100), but it

 could probably be redone in C with clever algorithms. This would be

 valuable, for example, if it was handle user-supplied exception

 dictionaries by integrating them into the rule table.[2]

    Once the rules are preprocessed, loading them is quite quick -

 about 200ms on a P100. It then hyphenates at about 40,000 words per

 second on a P100. I haven't benchmarked it against other

 implementations (both TeX and groff contain essentially the same

 algorithm), but expect that it runs quite a bit faster than any of

 them.

 Knuth's algorithm

    This section contains a brief explanation of Knuth's algorithm, in

 case you missed it from the TeX books. We'll use the semi-word

 "example" as our running example.

    Since the beginning and end of a word are special, the algorithm is

 actually run over the prepared word (prep_word in the source)

 ".example.". Knuths algorithm basically just does pattern matches from

 the rule set, then applies the matches. The patterns in this case that

 match are "xa", "xam", "mp", and "pl". These are actually stored as

 "x1a", "xam3", "4m1p", and "1p2l2". Whenever numbers appear between

 the letters, they are added in. If two (or more) patterns have numbers

 in the same place, the highest number wins. Here's the example:

  . e x a m p l e .

      x1a

      x a m3

         4m1p

           1p2l2

  -----------------

  . e x1a4m3p2l2e .

    Finally, hyphens are placed wherever odd numbers appear. They are,

 however, suppressed after the first letter and before the last letter

 of the word (TeX actually suppresses them before the next-to-last, as

 well). So, it's "ex-am-ple", which is correct.

    Knuth uses a trie to implement this. I.e. he stores each rule in a

 trie structure. For each position in the word, he searches the trie,

 searching for a match. Most patterns are short, so efficiency should

 be quite good.

 Theory of the algorithm

    The algorithm works as a slightly modified finite state machine.

 There are two kinds of transitions: those that consume one letter of

 input (which work just like your regular finite state machine), and

 "fallback" transitions, which don't consume any input. If no

 transition matching the next letter is found, the fallback is used.

 One way of looking at this is a form of compression of the transition

 tables - i.e. it behaves the same as a completely vanilla state

 machine in which the actual transition table of a node is made up of

 the union of transition tables of the node itself, plus its fallbacks.

    Each state is represented by a string. Thus, if the current state

 is "am" and the next letter is "p", then the next state is "amp".

 Fallback transitions go to states which chop off one or (sometimes)

 more letters from the beginning. For example, if none of the

 transitions from "amp" match the next letter, then it will fall back

 to "mp". Similarly, if none of the transitions from "mp" match the

 next letter, it will fall back to "m".

    Each state is also associated with a (possibly null) "match"

 string. This represents the union of all patterns which are

 right-justified substrings of the match string. I.e. the pattern "mp"

 is a right-justified substring of the state "amp", so it's numbers get

 added in. The actual calculation of this union is done by the

 Perl preprocessing script, but could probably be done in C just about

 as easily.

    Because each state transition either consumes one input character

 or shortens the state string by one character, the total number of

 state transitions is linear in the length of the word.

 [1] Documentations:

 Franklin M. Liang: Word Hy-phen-a-tion by Com-put-er.

 Stanford University, 1983. http://www.tug.org/docs/liang.

 László Németh: Automatic non-standard hyphenation in OpenOffice.org,

 TUGboat (27), 2006. No. 2., http://hunspell.sourceforge.net/tb87nemeth.pdf

 [2] There is the C version of pattern converter "substrings.c"

 in the distribution written by Nanning Buitenhuis. Unfortunatelly,

 this version hasn't handled the non standard extension of the

 algorithm, yet.