Tracing regularities plays a key role in data analysis for various areas of science, including coding and automata theory, formal language theory, combinatorics, molecular biology and many others. Part of the scientific process is understanding and explaining these regularities. A common notion to describe regularity in a string T is a cover or quasi-period, which is a string C for which every letter of T lies within some occurrence of C. In many applications finding exact repetitions is not sufficient, due to the presence of errors. In this paper we initiate the study of quasi-periodicity persistence under mismatch errors, and our goal is to characterize situations where a given quasiperiodic string remains quasi-periodic even after substitution errors have been introduced to the string. Our study results in proving necessary conditions as well as a theorem stating sufficient conditions for quasi-periodicity persistence. As an application, we are able to close the gap in understanding the complexity of Approximate Cover Problem (ACP) relaxations studied by [5, 4] and solve an open question.
|Title of host publication||29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018|
|Editors||Binhai Zhu, Gonzalo Navarro, David Sankoff|
|Publisher||Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing|
|Number of pages||375|
|State||Published - 1 May 2018|
|Event||29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018 - Qingdao, China|
Duration: 2 Jul 2018 → 4 Jul 2018
|Name||Leibniz International Proceedings in Informatics, LIPIcs|
|Conference||29th Annual Symposium on Combinatorial Pattern Matching, CPM 2018|
|Period||2/07/18 → 4/07/18|
Bibliographical notePublisher Copyright:
© 2018 Yoshifumi Sakai; licensed under Creative Commons License CC-BY.
- Approximate Cover