TY - JOUR

T1 - The Average Height of Catalan Trees by Counting Lattice Paths

AU - Dershowitz, Nachum

AU - Rinderknecht, Christian

N1 - Publisher Copyright:
© 2015, Taylor and Francis Ltd. All rights reserved.

PY - 2015

Y1 - 2015

N2 - The average height of Catalan trees of a given size is a structural parameter important in the analysis of algorithms, as it measures the expected maximum cost of a search in a tree. This parameter has been studied first with generating functions and complex variable theory, yielding an asymptotic approximation. Later on, real analysis was used instead of complex analysis. We have further reduced the conceptual difficulty by replacing generating functions with the enumeration of monotonic lattice paths, whose graphical representations make the derivation much more intuitive.

AB - The average height of Catalan trees of a given size is a structural parameter important in the analysis of algorithms, as it measures the expected maximum cost of a search in a tree. This parameter has been studied first with generating functions and complex variable theory, yielding an asymptotic approximation. Later on, real analysis was used instead of complex analysis. We have further reduced the conceptual difficulty by replacing generating functions with the enumeration of monotonic lattice paths, whose graphical representations make the derivation much more intuitive.

UR - http://www.scopus.com/inward/record.url?scp=85014770510&partnerID=8YFLogxK

U2 - 10.4169/MATH.MAG.88.3.187

DO - 10.4169/MATH.MAG.88.3.187

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AN - SCOPUS:85014770510

SN - 0025-570X

VL - 88

SP - 187

EP - 195

JO - Mathematics Magazine

JF - Mathematics Magazine

IS - 3

ER -