Determining the unique decodability of a string in linear time

Jiaxi Jin, Aryeh Kontorovich, Ari Trachtenberg

Research output: Contribution to conferencePaperpeer-review


Determining whether an unordered collection of overlapping substrings (called shingles) can be uniquely decoded into a consistent string is a problem common to a broad assortment of disciplines ranging from networking and information theory through cryptography and even genetic engineering and linguistics. We present three perspectives on this problem: a graph theoretic framework due to Pevzner, an automata theoretic approach from our previous work, and a new insight that yields an efficient streaming algorithm for determining whether a string of n characters over the alphabet Σ can be uniquely decoded from its two-character shingles; our online algorithm achieves an overall time complexity Θ(n + |Σ|) and space complexity O(|Σ|). As an application, we demonstrate how this algorithm can be adapted to larger, varying-size shingles for (empirically) efficient string reconciliation.

Original languageEnglish
Number of pages7
StatePublished - 16 May 2013
Event2013 Information Theory and Applications Workshop, ITA 2013 - San Diego, CA, United States
Duration: 10 Feb 201315 Feb 2013


Conference2013 Information Theory and Applications Workshop, ITA 2013
Country/TerritoryUnited States
CitySan Diego, CA

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Information Systems


Dive into the research topics of 'Determining the unique decodability of a string in linear time'. Together they form a unique fingerprint.

Cite this