2026-07-23T15:05:16Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:9497 2024-03-06T10:43:53Z ddc:004 open_access

A QPTAS for Gapless MEC Garg, Shilpa Mömke, Tobias approximation algorithms QPTAS minimum error correction segmentation computational biology We consider the problem Minimum Error Correction (MEC). A MEC instance is an n x m matrix M with entries from {0,1,-}. Feasible solutions are composed of two binary m-bit strings, together with an assignment of each row of M to one of the two strings. The objective is to minimize the number of mismatches (errors) where the row has a value that differs from the assigned solution string. The symbol "-" is a wildcard that matches both 0 and 1. A MEC instance is gapless, if in each row of M all binary entries are consecutive. Gapless-MEC is a relevant problem in computational biology, and it is closely related to segmentation problems that were introduced by {[}Kleinberg-Papadimitriou-Raghavan STOC'98{]} in the context of data mining. Without restrictions, it is known to be UG-hard to compute an O(1)-approximate solution to MEC. For both MEC and Gapless-MEC, the best polynomial time approximation algorithm has a logarithmic performance guarantee. We partially settle the approximation status of Gapless-MEC by providing a quasi-polynomial time approximation scheme (QPTAS). Additionally, for the relevant case where the binary part of a row is not contained in the binary part of another row, we provide a polynomial time approximation scheme (PTAS). Schloss Dagstuhl – Leibniz-Zentrum für Informatik Shilpa Garg and Tobias Mömke 2018 Is Part Of LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ESA.2018.34 urn:nbn:de:0030-drops-94978 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.34 eng https://creativecommons.org/licenses/by/3.0/legalcode