## Abstract

Tries are among the most versatile and widely used data structures on words. They are pertinent to the (internal) structure of (stored) words and several splitting procedures used in diverse contexts ranging from document taxonomy to IP addresses lookup, from data compression (i.e., Lempel-Ziv'77 scheme) to dynamic hashing, from partial-match queries to speech recognition, from leader election algorithms to distributed hashing tables and graph compression. While the performance of tries under a realistic probabilistic model is of significant importance, its analysis, even for simplest memoryless sources, has proved difficult. Rigorous findings about inherently complex parameters were rarely analyzed (with a few notable exceptions) under more realistic models of string generations. In this paper we meet these challenges: By a novel use of the contraction method combined with analytic techniques we prove a central limit theorem for the external path length of a trie under a general Markov source. In particular, our results apply to the Lempel-Ziv'77 code. We envision that the methods described here will have further applications to other trie parameters and data structures.

Original language | English |
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Title of host publication | Proceedings of the 24th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013 |

Publisher | Society for Industrial & Applied Mathematics (SIAM) |

Pages | 877-886 |

Number of pages | 10 |

ISBN (Print) | 9781611972511 |

Publication status | Published - 2013 |

Externally published | Yes |

Event | ACM/SIAM Symposium on Discrete Algorithms 2013 - Astor Crown Plaza Hotel, New Orleans, United States of America Duration: 6 Jan 2013 → 8 Jan 2013 Conference number: 24th http://www.siam.org/meetings/da13/ |

### Conference

Conference | ACM/SIAM Symposium on Discrete Algorithms 2013 |
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Abbreviated title | SODA 2013 |

Country | United States of America |

City | New Orleans |

Period | 6/01/13 → 8/01/13 |

Internet address |