Longest Common Subsequence on Weighted Sequences.

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review


We consider the general problem of the Longest Common Subsequence (LCS) on weighted sequences. Weighted sequences are an extension of classical strings, where in each position every letter of the alphabet may occur with some probability. Previous results presented a PTAS and noticed that no FPTAS is possible unless P=NP. In this paper we essentially close the gap between upper and lower bounds by improving both. First of all, we provide an EPTAS for bounded alphabets (which is the most natural case), and prove that there does not exist any EPTAS for unbounded alphabets unless FPT=W[1]. Furthermore, under the Exponential Time Hypothesis, we provide a lower bound which shows that no significantly better PTAS can exist for unbounded alphabets. As a side note, we prove that it is sufficient to work with only one threshold in the general variant of the problem.
Original languageEnglish
Title of host publicationLongest Common Subsequence on Weighted Sequences.
Number of pages15
PublisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik
Publication dateJun 2020
ISBN (Print)978-3-95977-149-8
Publication statusPublished - Jun 2020
Externally publishedYes
SeriesLeibniz International Proceedings in Informatics, LIPIcs

Bibliographical note

Received the Alberto Apostolico Best Paper Award.

ID: 257869307