2013 | OriginalPaper | Buchkapitel
Pattern Matching with Non Overlapping Reversals - Approximation and On-line Algorithms
verfasst von : Amihood Amir, Benny Porat
Erschienen in: Algorithms and Computation
Verlag: Springer Berlin Heidelberg
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The
Sorting by Reversals
Problem is known to be
$\cal{NP}$
-hard. A simplification,
Sorting by Signed Reversals
is polynomially computable. Motivated by the Pattern Matching with Rearrangements model, we consider
Pattern Matching with Reversals
. Since this is a generalization of the Sorting by Reversals problem, it is clearly
${\cal NP}$
-hard. We, therefore consider the simplification where reversals cannot overlap. Such a constrained version has been researched in the past for various metrics in the rearrangement model - the swap metric and the interchange metric. We show that the constrained problem can be solved in linear time. We then consider the
Approximate Pattern Matching with non-overlapping Reversals
problem, i.e. where mismatch errors are introduced. We show that the problem can be solved in quadratic time and space. Finally, we consider the on-line version of the problem. We introduce a novel signature for palindromes and show that it has a pleasing behavior, similar to the Karp-Rabin signature. It allows solving the
Pattern Matching with non-overlapping Reversals
problem on-line in linear time w.h.p.