eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-03-02
15:1
15:13
10.4230/LIPIcs.IPEC.2017.15
article
Tight Conditional Lower Bounds for Longest Common Increasing Subsequence
Duraj, Lech
Künnemann, Marvin
Polak, Adam
We consider the canonical generalization of the well-studied Longest Increasing Subsequence problem to multiple sequences, called k-LCIS: Given k integer sequences X_1,...,X_k of length at most n, the task is to determine the length of the longest common subsequence of X_1,...,X_k that is also strictly increasing. Especially for the case of k=2 (called LCIS for short), several algorithms have been proposed that require quadratic time in the worst case.
Assuming the Strong Exponential Time Hypothesis (SETH), we prove a tight lower bound, specifically, that no algorithm solves LCIS in (strongly) subquadratic time. Interestingly, the proof makes no use of normalization tricks common to hardness proofs for similar problems such as LCS. We further strengthen this lower bound to rule out O((nL)^{1-epsilon}) time algorithms for LCIS, where L denotes the solution size, and to rule out O(n^{k-epsilon}) time algorithms for k-LCIS. We obtain the same conditional lower bounds for the related Longest Common Weakly Increasing Subsequence problem.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol089-ipec2017/LIPIcs.IPEC.2017.15/LIPIcs.IPEC.2017.15.pdf
fine-grained complexity
combinatorial pattern matching
sequence alignments
parameterized complexity
SETH