eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-03-04
41:1
41:18
10.4230/LIPIcs.STACS.2020.41
article
A Sub-Quadratic Algorithm for the Longest Common Increasing Subsequence Problem
Duraj, Lech
1
https://orcid.org/0000-0002-0004-3751
Theoretical Computer Science, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland
The Longest Common Increasing Subsequence problem (LCIS) is a natural variant of the celebrated Longest Common Subsequence (LCS) problem. For LCIS, as well as for LCS, there is an ?(n²)-time algorithm and a SETH-based conditional lower bound of ?(n^{2-ε}). For LCS, there is also the Masek-Paterson ?(n²/log n)-time algorithm, which does not seem to adapt to LCIS in any obvious way. Hence, a natural question arises: does any (slightly) sub-quadratic algorithm exist for the Longest Common Increasing Subsequence problem? We answer this question positively, presenting a ?(n²/log^a n)-time algorithm for a = 1/6-o(1). The algorithm is not based on memorizing small chunks of data (often used for logarithmic speedups, including the "Four Russians Trick" in LCS), but rather utilizes a new technique, bounding the number of significant symbol matches between the two sequences.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol154-stacs2020/LIPIcs.STACS.2020.41/LIPIcs.STACS.2020.41.pdf
longest common increasing subsequence
log-shaving
matching pairs