Cycle detection and correction

Amihood Amir, Estrella Eisenberg, Avivit Levy, Ely Porat, Natalie Shapira

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations


Assume that a natural cyclic phenomenon has been measured, but the data is corrupted by errors. The type of corruption is application-dependent and may be caused by measurements errors, or natural features of the phenomenon. This paper studies the problem of recovering the correct cycle from data corrupted by various error models, formally defined as the period recovery problem. Specifically, we define a metric property which we call pseudo-locality and study the period recovery problem under pseudo-local metrics. Examples of pseudo-local metrics are the Hamming distance, the swap distance, and the interchange (or Cayley) distance. We show that for pseudo-local metrics, periodicity is a powerful property allowing detecting the original cycle and correcting the data, under suitable conditions. Some surprising features of our algorithm are that we can efficiently identify the period in the corrupted data, up to a number of possibilities logarithmic in the length of the data string, even for metrics whose calculation is -hard. For the Hamming metric we can reconstruct the corrupted data in near linear time even for unbounded alphabets. This result is achieved using the property of separation in the self-convolution vector and Reed-Solomon codes. Finally, we employ our techniques beyond the scope of pseudo-local metrics and give a recovery algorithm for the non pseudo-local Levenshtein edit metric.

Original languageEnglish
Title of host publicationAutomata, Languages and Programming - 37th International Colloquium, ICALP 2010, Proceedings
Number of pages12
EditionPART 1
StatePublished - 2010
Event37th International Colloquium on Automata, Languages and Programming, ICALP 2010 - Bordeaux, France
Duration: 6 Jul 201010 Jul 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume6198 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference37th International Colloquium on Automata, Languages and Programming, ICALP 2010


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