In delicious.com, users are able to bookmark website links with
various meaningful tags, such as for a link titled "Sorting Algorithm
Animations", one can tag it as "algorithm", "sort", and later (maybe
after months) find this previously tagged bookmark by searching either
"sort" or "algorithm". It greatly improves our way of keeping and
organizing knowledge.

Also in delicious.com, when you search for a tag, say "algorithm", it
is able to show all the associated tags to "algorithm". For example,
the user has several bookmarks, and they are tagged as following:

Link1: algorithm sort
Link2: algorithm heap stack
Link3: algorithm heap fantastic
Link4: database architecture

Then, the associated tags to "algorithm" will be "sort", "heap“,
”stack", "fantastic" (all tags that showed up together with
"algorithm" in bookmarks).

Further, we can also find associated tags to multiple tags. For
example, when I search "algorithm" and "heap", the associated tags to
these words will be "stack" and "fantastic".

So, associated tags are tags that showed up together in some bookmarks
with the given tags.

The problem is how to implement this associated tag searching.

The naive way will be first searching all the links that have the
given tags (when I search for "algorithm" and "heap", it will return
Link2 and Link3), then by looking through all the returned links, I
get the tags that are associated to "algorithm" and "heap".

This naive way surely works, but it's very time inefficient.

Also, we cannot use indexing of tags. Say there're 3 links, each with
2 tags:

L1: t1, t2
L2: t1, t3
L3: t2, t3

Then, if I search for associated tags to both "t1, t2", I'll get
result as "t3", since t3 is indexed by both t1 in L2, and indexed by
t2 in L3. But in fact there's no link that contains all t1,t2 and t3,
so according to definition t3 should not appear in the result of
associated tags.

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