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Erschienen in:
2010 | OriginalPaper | Buchkapitel
String Matching with Variable Length Gaps
verfasst von : Philip Bille, Inge Li Gørtz, Hjalte Wedel Vildhøj, David Kofoed Wind
Erschienen in: String Processing and Information Retrieval
Verlag: Springer Berlin Heidelberg
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We consider string matching with variable length gaps. Given a string
T
and a pattern
P
consisting of strings separated by variable length gaps (arbitrary strings of length in a specified range), the problem is to find all ending positions of substrings in
T
that match
P
. This problem is a basic primitive in computational biology applications. Let
m
and
n
be the lengths of
P
and
T
, respectively, and let
k
be the number of strings in
P
. We present a new algorithm achieving time
O
((
n
+
m
)log
k
+
α
) and space
O
(
m
+
A
), where
A
is the sum of the lower bounds of the lengths of the gaps in
P
and
α
is the total number of occurrences of the strings in
P
within
T
. Compared to the previous results this bound essentially achieves the best known time and space complexities simultaneously. Consequently, our algorithm obtains the best known bounds for almost all combinations of
m
,
n
,
k
,
A
, and
α
. Our algorithm is surprisingly simple and straightforward to implement.