Anzeige
Erschienen in:
2006 | OriginalPaper | Buchkapitel
Faster Algorithms for Computing Longest Common Increasing Subsequences
verfasst von : Gerth Stølting Brodal, Kanela Kaligosi, Irit Katriel, Martin Kutz
Erschienen in: Combinatorial Pattern Matching
Verlag: Springer Berlin Heidelberg
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
We present algorithms for finding a longest common increasing subsequence of two or more input sequences. For two sequences of lengths
m
and
n
, where
m
≥
n
, we present an algorithm with an output-dependent expected running time of
$O((m+n\ell) \log\log \sigma + {\ensuremath{\mathit{Sort}}})$
and
O
(
m
) space, where ℓ is the length of an LCIS,
σ
is the size of the alphabet, and
${\ensuremath{\mathit{Sort}}}$
is the time to sort each input sequence. For
k
≥3 length-
n
sequences we present an algorithm which improves the previous best bound by more than a factor
k
for many inputs. In both cases, our algorithms are conceptually quite simple but rely on existing sophisticated data structures. Finally, we introduce the problem of longest common weakly-increasing (or non-decreasing) subsequences (LCWIS), for which we present an
O
(
m
+
n
log
n
)-time algorithm for the 3-letter alphabet case. For the extensively studied longest common subsequence problem, comparable speedups have not been achieved for small alphabets.