Article ID Journal Published Year Pages File Type
427573 Information Processing Letters 2013 6 Pages PDF
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≥nm≥n denote lengths of the sequences.

► We search for longest common subsequence of two sequences that is sorted, i.e. weakly increasing. ► An algorithm of linear time complexity for sequences over 3-letter alphabet is presented, improving previously known O(nloglogn) algorithm. ► Our algorithm uses simple list-like data structures instead of complex van Emde-Boas queues.

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Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
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