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1Brief explanation of the hyphenation algorithm herein.[1]
2
3Raph Levien <raph@acm.org>
44 Aug 1998
5
6   The hyphenation algorithm is basically the same as Knuth's TeX
7algorithm. However, the implementation is quite a bit faster.
8
9   The hyphenation files from TeX can almost be used directly. There
10is a preprocessing step, however. If you don't do the preprocessing
11step, you'll get bad hyphenations (i.e. a silent failure).
12
13   Start with a file such as hyphen.us. This is the TeX ushyph1.tex
14file, with the exception dictionary encoded using the same rules as
15the main portion of the file. Any line beginning with % is a comment.
16Each other line should contain exactly one rule.
17
18   Then, do the preprocessing - "perl substrings.pl hyphen.us". The
19resulting file is hyphen.mashed. It's in Perl, and it's fairly slow
20(it uses brute force algorithms; about 17 seconds on a P100), but it
21could probably be redone in C with clever algorithms. This would be
22valuable, for example, if it was handle user-supplied exception
23dictionaries by integrating them into the rule table.[2]
24
25   Once the rules are preprocessed, loading them is quite quick -
26about 200ms on a P100. It then hyphenates at about 40,000 words per
27second on a P100. I haven't benchmarked it against other
28implementations (both TeX and groff contain essentially the same
29algorithm), but expect that it runs quite a bit faster than any of
30them.
31
32Knuth's algorithm
33
34   This section contains a brief explanation of Knuth's algorithm, in
35case you missed it from the TeX books. We'll use the semi-word
36"example" as our running example.
37
38   Since the beginning and end of a word are special, the algorithm is
39actually run over the prepared word (prep_word in the source)
40".example.". Knuths algorithm basically just does pattern matches from
41the rule set, then applies the matches. The patterns in this case that
42match are "xa", "xam", "mp", and "pl". These are actually stored as
43"x1a", "xam3", "4m1p", and "1p2l2". Whenever numbers appear between
44the letters, they are added in. If two (or more) patterns have numbers
45in the same place, the highest number wins. Here's the example:
46
47 . e x a m p l e .
48     x1a
49     x a m3
50        4m1p
51          1p2l2
52 -----------------
53 . e x1a4m3p2l2e .
54
55   Finally, hyphens are placed wherever odd numbers appear. They are,
56however, suppressed after the first letter and before the last letter
57of the word (TeX actually suppresses them before the next-to-last, as
58well). So, it's "ex-am-ple", which is correct.
59
60   Knuth uses a trie to implement this. I.e. he stores each rule in a
61trie structure. For each position in the word, he searches the trie,
62searching for a match. Most patterns are short, so efficiency should
63be quite good.
64
65Theory of the algorithm
66
67   The algorithm works as a slightly modified finite state machine.
68There are two kinds of transitions: those that consume one letter of
69input (which work just like your regular finite state machine), and
70"fallback" transitions, which don't consume any input. If no
71transition matching the next letter is found, the fallback is used.
72One way of looking at this is a form of compression of the transition
73tables - i.e. it behaves the same as a completely vanilla state
74machine in which the actual transition table of a node is made up of
75the union of transition tables of the node itself, plus its fallbacks.
76
77   Each state is represented by a string. Thus, if the current state
78is "am" and the next letter is "p", then the next state is "amp".
79Fallback transitions go to states which chop off one or (sometimes)
80more letters from the beginning. For example, if none of the
81transitions from "amp" match the next letter, then it will fall back
82to "mp". Similarly, if none of the transitions from "mp" match the
83next letter, it will fall back to "m".
84
85   Each state is also associated with a (possibly null) "match"
86string. This represents the union of all patterns which are
87right-justified substrings of the match string. I.e. the pattern "mp"
88is a right-justified substring of the state "amp", so it's numbers get
89added in. The actual calculation of this union is done by the
90Perl preprocessing script, but could probably be done in C just about
91as easily.
92
93   Because each state transition either consumes one input character
94or shortens the state string by one character, the total number of
95state transitions is linear in the length of the word.
96
97[1] Documentations:
98
99Franklin M. Liang: Word Hy-phen-a-tion by Com-put-er.
100Stanford University, 1983. http://www.tug.org/docs/liang.
101
102László Németh: Automatic non-standard hyphenation in OpenOffice.org,
103TUGboat (27), 2006. No. 2., http://hunspell.sourceforge.net/tb87nemeth.pdf
104
105[2] There is the C version of pattern converter "substrings.c"
106in the distribution written by Nanning Buitenhuis. Unfortunatelly,
107this version hasn't handled the non standard extension of the
108algorithm, yet.
109