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).
@InProceedings{agrawal_et_al:LIPIcs.ISAAC.2020.4, author = {Agrawal, Anadi and Gawrychowski, Pawe{\l}}, title = {{A Faster Subquadratic Algorithm for the Longest Common Increasing Subsequence Problem}}, booktitle = {31st International Symposium on Algorithms and Computation (ISAAC 2020)}, pages = {4:1--4:12}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-173-3}, ISSN = {1868-8969}, year = {2020}, volume = {181}, editor = {Cao, Yixin and Cheng, Siu-Wing and Li, Minming}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.4}, URN = {urn:nbn:de:0030-drops-133487}, doi = {10.4230/LIPIcs.ISAAC.2020.4}, annote = {Keywords: Longest Common Increasing Subsequence, Four Russians} }
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