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Reconstructing Words Using Queries on Subwords or Factors

Authors Gwenaël Richomme , Matthieu Rosenfeld

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ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Mathematics of computing → Combinatorics on words
Keywords
  • Word reconstruction
  • Subwords
  • Factors

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Abstract

We study word reconstruction problems. Improving a previous result by P. Fleischmann, M. Lejeune, F. Manea, D. Nowotka and M. Rigo, we prove that, for any unknown word w of length n over an alphabet of cardinality k, w can be reconstructed from the number of occurrences as subwords (or scattered factors) of O(k²√{nlog₂(n)}) words. Two previous upper bounds obtained by S. S. Skiena and G. Sundaram are also slightly improved: one when considering information on the existence of subwords instead of on the numbers of their occurrences, and, the other when considering information on the existence of factors.

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Gwenaël Richomme and Matthieu Rosenfeld. Reconstructing Words Using Queries on Subwords or Factors. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 52:1-52:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.STACS.2023.52

Author Details

Gwenaël Richomme
  • LIRMM, Université Paul-Valéry Montpellier 3, Université de Montpellier, CNRS, Montpellier, France
Matthieu Rosenfeld
  • LIRMM, Université de Montpellier, CNRS, Montpellier, France

Acknowledgements

Authors thank Victor Poupet for useful discussions. Many thanks also for the referees for their accurate reading and their valuable suggestions.

References

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