eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-12-04
4:1
4:12
10.4230/LIPIcs.ISAAC.2020.4
article
A Faster Subquadratic Algorithm for the Longest Common Increasing Subsequence Problem
Agrawal, Anadi
1
Gawrychowski, Paweł
1
Institute of Computer Science, University of Wrocław, Poland
The Longest Common Increasing Subsequence (LCIS) is a variant of the classical Longest Common Subsequence (LCS), in which we additionally require the common subsequence to be strictly increasing. While the well-known "Four Russians" technique can be used to find LCS in subquadratic time, it does not seem directly applicable to LCIS. Recently, Duraj [STACS 2020] used a completely different method based on the combinatorial properties of LCIS to design an 𝒪(n²(log log n)²/log^{1/6}n) time algorithm. We show that an approach based on exploiting tabulation (more involved than "Four Russians") can be used to construct an asymptotically faster 𝒪(n² log log n/√{log n}) time algorithm. As our solution avoids using the specific combinatorial properties of LCIS, it can be also adapted for the Longest Common Weakly Increasing Subsequence (LCWIS).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol181-isaac2020/LIPIcs.ISAAC.2020.4/LIPIcs.ISAAC.2020.4.pdf
Longest Common Increasing Subsequence
Four Russians