PMID: 11909185Mar 23, 2002Paper

Extreme value statistics and traveling fronts: application to computer science

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
S N Majumdar, P L Krapivsky

Abstract

We study the statistics of height and balanced height in the binary search tree problem in computer science. The search tree problem is first mapped to a fragmentation problem that is then further mapped to a modified directed polymer problem on a Cayley tree. We employ the techniques of traveling fronts to solve the polymer problem and translate back to derive exact asymptotic properties in the original search tree problem. The second mapping allows us not only to again derive the already known results for random binary trees but to obtain exact results for search trees where the entries arrive according to an arbitrary distribution, not necessarily randomly. Besides it allows us to derive the asymptotic shape of the full probability distribution of height and not just its moments. Our results are then generalized to m-ary search trees with arbitrary distribution.

References

May 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·S N CoppersmithT A Witten
Jan 4, 2001·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·S N Majumdar, P L Krapivsky
Oct 3, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·E Ben-NaimS N Majumdar
Nov 3, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·D DasS N Majumdar

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Citations

Aug 16, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·J F MuzyA Kozhemyak
Mar 16, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·G GyörgyiZ Rácz
May 16, 2007·Physical Review Letters·Sanjib Sabhapandit, Satya N Majumdar
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Cécile Monthus, Thomas Garel
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ioana Bena, Satya N Majumdar
Dec 4, 2013·Genetics·Juan Venegas-OrtizMartin R Evans
Nov 5, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Debabrata Panja
Apr 4, 2017·Chaos·A AliakbariM J Salehi
May 17, 2017·Physical Review. E·Thomas Gueudré
Apr 4, 2015·Physical Review Letters·Eren Metin ElçiNikolaos G Fytas
Oct 4, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Satya N Majumdar
Jun 13, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N R Moloney, J Davidsen
Oct 4, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·P L Krapivsky, E Ben-Naim
Mar 20, 2021·Physical Review. E·Michel BauerKirone Mallick
Jun 18, 2021·Physical Review. E·Prashant Singh, Arnab Pal

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