24 the structure of generalized
suffix tree is crucially used to design
a linear machine-word data structure
to return the top-k most frequent documents containing a pattern p in time
nearly linear in pattern size.
One surprising variant of the suffix
tree was introduced by Brenda Baker
for purposes of detection of plagiarism in student reports as well as optimization in software development.
This variant of pattern matching,
called “parameterized matching,” enables one to find program segments
that are identical up to a systematic
change of parameters, or substrings
that are identical up to a systematic
relabeling or permutation of the characters in the alphabet. One obvious
extension of the notion of a suffix
tree is to more than one dimension,
albeit the mechanics of the extension
itself are far from obvious.
more distant relatives, one finds
“wavelet trees.” Originally proposed
as a representation of compressed
20 wavelet trees enable
one to perform on general alphabets
the ranking and selection primitives
previously limited to bit vectors, and
The list could go on and on, but the
scope of this article was not meant
to be exhaustive. Actually, after 40
years of unrelenting developments,
it is fair to assume the list will continue to grow. Open problems also
abound. For instance, many of the
observed sequences are expressed in
numbers rather than characters, and
in both cases are affected by various
types of errors. While the outcome of
a two-character comparison is just
one bit, two numbers can be more or
less close, depending on their difference or some other metric. Likewise,
two text strings can be more or less
similar, depending on the number of
elementary steps necessary to change
one in the other. The most disruptive
aspect of this framework is the loss of
the transitivity property that leads to
the most efficient exact string matching solutions. And yet indexes capable of supporting fast and elegant approximate pattern queries of the kind
just highlighted would be immensely
useful. Hopefully, they will come up
soon and, in time, have their own 40th
Acknowledgments. We are grateful to Ed McCreight, Ronnie Martin,
Vaughan Pratt, Peter Weiner, and Jacob Ziv for discussions and help. We
are indebted to the referees for their
careful scrutiny of an earlier version
of this article, which led to many improvements.
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Alberto Apostolico held joint appointments with Georgia
Tech’s School of Computational Science and Engineering
School of Interactive computing as a professor and a
researcher. He passed away on July 20, 2015.
Maxime Crochemore ( firstname.lastname@example.org)
is a professor at King’s College London and Université
Martin Farach-Colton ( email@example.com) is a
professor in the Department of Computer Science at
Rutgers University, Piscataway, NJ.
Zvi Galil ( firstname.lastname@example.org) is Dean of the College of
Computing at Georgia Institute of Technology, Atlanta, GA.
S. Muthukrishnan ( email@example.com) is a professor
in the Department of Computer Science at Rutgers
University, Piscataway, NJ.
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