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Dichotomic Selection on Words: A Probabilistic Analysis

Authors Ali Akhavi, Julien Clément, Dimitri Darthenay, Loïck Lhote, Brigitte Vallée

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Subject Classification

ACM Subject Classification
  • Theory of computation → Data structures design and analysis
  • Theory of computation → Randomness, geometry and discrete structures
  • Theory of computation → Sorting and searching
  • Theory of computation → Pattern matching
  • Mathematics of computing → Combinatorics on words
  • Mathematics of computing → Discrete mathematics
Keywords
  • dichotomic selection
  • text algorithms
  • analysis of algorithms
  • average case analysis of algorithms
  • trie
  • suffix array
  • lcp-array
  • information theory
  • numeration process
  • sources
  • entropy
  • coincidence
  • analytic combinatorics
  • depoissonization techniques

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Abstract

The paper studies the behaviour of selection algorithms that are based on dichotomy principles. On the entry formed by an ordered list L and a searched element x not in L, they return the interval of the list L the element x belongs to. We focus here on the case of words, where dichotomy principles lead to a selection algorithm designed by Crochemore, Hancart and Lecroq, which appears to be "quasi-optimal". We perform a probabilistic analysis of this algorithm that exhibits its quasi-optimality on average.

Cite As Get BibTex

Ali Akhavi, Julien Clément, Dimitri Darthenay, Loïck Lhote, and Brigitte Vallée. Dichotomic Selection on Words: A Probabilistic Analysis. In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 128, pp. 19:1-19:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.CPM.2019.19

Author Details

Ali Akhavi
  • GREYC (Normandie Université, Unicaen, EnsiCaen, Cnrs), 14000, Caen, France
Julien Clément
  • GREYC (Normandie Université, Unicaen, EnsiCaen, Cnrs), 14000, Caen, France
Dimitri Darthenay
  • GREYC (Normandie Université, Unicaen, EnsiCaen, Cnrs), 14000, Caen, France
Loïck Lhote
  • GREYC (Normandie Université, Unicaen, EnsiCaen, Cnrs), 14000, Caen, France
Brigitte Vallée
  • GREYC (Normandie Université, Unicaen, EnsiCaen, Cnrs), 14000, Caen, France

Funding

Projects: DynA3S, CoDys, MetaConc (ANR), AleaEnAmSud (STICAmSud).

Acknowledgements

We thank Pablo Rotondo for many interesting discussions. We also thank anonymous reviewers for pointing us to bibliographic references.

References

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