A linear algorithm for 3-letter longest common weakly increasing subsequence

Authors:
Lech Duraj
Affiliations:
Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Prof. St. Lojasiewicza 6, 30-348 Krakow, Poland
Venue:
Information Processing Letters
Year:
2013

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Abstract

The problem of finding a longest weakly increasing common subsequence (LCWIS) of two sequences is a variant of the popular longest common subsequence (LCS) problem. While there are no known methods to find LCS in truly sub-quadratic time, there are faster algorithms to compute LCWIS if the alphabet size is small enough. We present a linear-time algorithm finding LCWIS over 3-letter alphabet. Up to now, the fastest known algorithm was O(min{m+nlogn,mloglogm}), where m=n denote lengths of the sequences.