Faster Algorithms for Computing Longest Common Increasing Subsequences
Gerth Stølting Brodal
December 2005 |

## Abstract:
We present algorithms for finding a longest common increasing
subsequence of two or more input sequences. For two sequences of lengths
and , where , we present an algorithm with an output-dependent
expected running time of
and
space, where is the length of a LCIS, is the size of
the alphabet, and is the time to sort each input
sequence.For length- sequences we present an algorithm
running time
, which improves the
previous best bound by more than a factor 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 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.
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Last modified: 2005-12-15 by webmaster.