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I found the best anagram in English (2017)

I found the best anagram in English

I planned to publish this last week sometime but then I wrote a line
of code with three errors
and that
took over the blog.

A few years ago I mentioned in passing that
in the 1990s I had constructed a listing of all the anagrams
in Webster’s Second International dictionary. (The
Webster’s headword list was available

This was easy to do, even at the time, when the word list itself, at
2.5 megabytes, was a file of significant size. Perl and its cousins
were not yet common; in those days I used Awk. But the task is not
very different in any reasonable language:

  # Process word list
  while (my $word = <>) {
    chomp $word;
    my $sorted = join "", sort split //, $word;  # normal form
    push @{$anagrams{$sorted}}, $word;

  for my $words (values %anagrams) {
      print "@$wordsn" if @$words > 1;

The key technique is to reduce each word to a normal form so that
two words have the same normal form if and only if they are anagrams
of one another. In this case we do this by sorting the letters into
alphabetical order, so that both megalodon and moonglade become

Then we insert the words into a (hash | associative array |
dictionary), keyed by their normal forms, and two or more words are
anagrams if they fall into the same hash bucket. (There is some
discussion of this technique in Higher-Order
pages 218–219 and elsewhere.)

(The thing you do not want to do is to compute every permutation of
the letters of each word, looking for permutations that appear in the
word list. That is akin to sorting a list by computing every
permutation of the list and looking for the one that is sorted. I
wouldn’t have mentioned this, but someone on StackExchange actually
asked this question.)

Anyway, I digress. This article is about how I was unhappy with the
results of the simple procedure above. From the Webster’s Second
list, which contains about 234,000 words, it finds about 14,000
anagram sets (some with more than two words), consisting of 46,351
pairs of anagrams. The list starts with

aal ala

and ends with

zolotink zolotnik

which exemplify the problems with this simple approach: many of the
46,351 anagrams are obvious, uninteresting or even trivial. There
must be good ones in the list, but how to find them?

I looked in the list to find the longest anagrams, but they were also

cholecystoduodenostomy duodenocholecystostomy

(Webster’s Second contains a large amount of scientific and medical
jargon. A cholecystoduodenostomy is a surgical operation to
create a channel between the gall bladder (cholecysto-) and the
duodenum (duodeno-). A duodenocholecystostomy is the same thing.)

This example made clear at least one of the problems with boring
anagrams: it’s not that they are too short, it’s that they are too
simple. Cholecystoduodenostomy and duodenocholecystostomy are 22
letters long, but the anagrammatic relation between them is obvious:
chop cholecystoduodenostomy into three parts:

cholecysto duodeno stomy

and rearrange the first two:

duodeno cholecysto stomy

and there you have it.

This gave me the idea to score a pair of anagrams according to how
many chunks one had to be cut into in order to rearrange it to make
the other one. On this plan, the “cholecystoduodenostomy / duodenocholecystostomy” pair would score 3,
just barely above the minimum possible score of 2. Something even a
tiny bit more interesting, say “abler / blare” would score higher, in
this case 4. Even if this strategy didn’t lead me directly to the
most interesting anagrams, it would be a big step in the right
direction, allowing me to eliminate the least interesting.

This rule would judge both “aal / ala” and “zolotink / zolotnik” as
being uninteresting (scores 2 and 4 respectively), which is a good
outcome. Note that some other boring-anagram problems can be seen as
special cases of this one. For example, short anagrams never need to
be cut into many parts: no four-letter anagrams can score higher
than 4. The trivial anagramming of a word to itself always scores 1,
and nontrivial anagrams always score more than this.

So what we need to do is: for each anagram pair, say
acrididae (grasshoppers)
and cidaridae (sea
urchins), find the smallest number of chunks into which we can chop
acrididae so that the chunks can be rearranged into cidaridae.

One could do this with a clever algorithm, if one were available.
There is a clever algorithm,
based on finding maximum independent sets in a certain graph. (More
about this tomorrow.) I did not find this algorithm at the time; nor
did I try. Instead, I used a brute-force search. Or rather, I used a
very small amount of cleverness to reduce the search space, and then
used brute-force search to search the reduced space.

Let’s consider a example, scoring the anagram “abscise / scabies”.
You do not have to consider every possible permutation of
abscise. Rather, there are only two possible mappings from the
letters of abscise to the letters of scabies. You know that the
C must map to the C, the A must map to the A, and so
forth. The only question is whether the first S of abscise maps to
the first or to the second S of scabies. The first mapping gives

and the second gives us

because the S and the C no longer go to adjoining positions. So
the minimum number of chunks is 5, and this anagram pair gets a score
of 5.

To fully analyze cholecystoduodenostomy by this method required considering 7680
mappings. (120 ways to map the five O‘s × 2 ways to map the two
C‘s × 2 ways to map the two D‘s, etc.) In the 1990s this took a
while, but not prohibitively long, and it worked well enough that I
did not bother to try to find a better algorithm. In 2016 it would
probably still run quicker than implementing the maximum independent
set algorithm. Unfortunately I have lost the code that I wrote then
so I can’t compare.

Assigning scores in this way produced a scored anagram list which

2 aal ala

and ended

4 zolotink zolotnik

and somewhere in the middle was

3 cholecystoduodenostomy duodenocholecystostomy

all poor scores. But sorted by score, there were treasures at the
end, and the clear winner was

14 cinematographer megachiropteran

I declare this the single best anagram in English. It is 15 letters
long, and the only letters that stay together are the E and the R.
“Cinematographer” is as familiar as a 15-letter word can be, and
“megachiropteran” means a giant bat. GIANT BAT! DEATH FROM

And there is no serious competition. There was another 14-pointer,
but both its words are Webster’s Second jargon that nobody knows:

14 rotundifoliate titanofluoride

There are no score 13 pairs, and the score 12 pairs are all obscure.
So this is the winner, and a deserving winner it is.

I think there is something in the list to make everyone happy. If you
are the type of person who enjoys anagrams, the list rewards casual
browsing. A few examples:

7 admirer married

7 admires sidearm

8 negativism timesaving

8 peripatetic precipitate

8 scepters respects

8 shortened threnodes

8 soapstone teaspoons

9 earringed grenadier

9 excitation intoxicate

9 integrals triangles

9 ivoriness revisions

9 masculine calumnies

10 coprophagist topographics

10 chuprassie haruspices

10 citronella interlocal

11 clitoridean directional

11 dispensable piebaldness

“Clitoridean / directional” has been one of my favorites for years.
But my favorite of all, although it scores only 6, is

6 yttrious touristy

I think I might love it just because the word yttrious is so
delightful. (What a debt we owe to Ytterby,

I also rather like

5 notaries senorita

which shows that even some of the low-scorers can be worth looking at.
Clearly my chunk score is not the end of the story, because “notaries
/ senorita” should score better than “abets / baste” (which is boring)
or “Acephali / Phacelia” (whatever those are), also 5-pointers. The
length of the words should be worth something, and the familiarity of
the words should be worth even more.

Here are the results:

In former times there was a restaurant in Philadelphia named
“Soupmaster”. My best unassisted anagram discovery was noticing
that this is an anagram of “mousetraps”.

[ Addendum 20170222: There is a followup article
comparing the two algorithms I wrote for computing scores. ]

[ Addendum 20170222: An earlier version of this article mentioned the
putative 11-pointer “endometritria / intermediator”. The word
“endometritria” seemed pretty strange, and I did look into it before I
published the article, but not carefully enough. When Philip Cohen
wrote to me to question it, I investigated more carefully, and
discovered that it had been an error in an early
WordNet release, corrected (to
“endometria”) in version 1.6. I didn’t remember that I had used
WordNet’s word lists, but I am not surprised to discover that I did. ]

[ Addendum 20170223: More about this ]

[ Addendum 20170507: Slides from my !!Con 2017 talk are now available. ]

[ Addendum 20170511: A large amount of miscellaneous related material ]

[Other articles in category /lang]
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