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Traveling front solutions to directed diffusion-limited aggregation, digital search trees, and the Lempel-Ziv data compression algorithm

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 05 Aug 2003Embargo end date: 01 Jan 2003 English Publisher:American Physical Society (APS)Journal:Physical Review E, volume 68 (issn: 1063-651X, eissn: 1095-3787, Copyright policy )
Authors: Majumdar, Satya N.;

doi: 10.1103/physreve.68.026103 , 10.48550/arxiv.cond-mat/0305097

pmid: 14525045

arXiv: cond-mat/0305097

Traveling front solutions to directed diffusion-limited aggregation, digital search trees, and the Lempel-Ziv data compression algorithm

Abstract

We use the traveling front approach to derive exact asymptotic results for the statistics of the number of particles in a class of directed diffusion limited aggregation models on a Cayley tree. We point out that some aspects of these models are closely connected to two different problems in computer science, namely the digital search tree problem in data structures and the Lempel-Ziv algorithm for data compression. The statistics of the number of particles studied here is related to the statistics of height in digital search trees which, in turn, is related to the statistics of the length of the longest word formed by the Lempel-Ziv algorithm. Implications of our results to these computer science problems are pointed out.

Revtex, 11 pages, 3 .eps figures included

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Keywords

FOS: Computer and information sciences, Statistical Mechanics (cond-mat.stat-mech), Computer Science - Data Structures and Algorithms, FOS: Physical sciences, Data Structures and Algorithms (cs.DS), Condensed Matter - Statistical Mechanics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
30
Top 10%
Top 10%
Top 10%
Green