Hypergeometrics and the Cost Structure of Quadtrees Hypergeometrics and the Cost Structure of Quadtrees Hypergeometrics and the Cost Structure of Quadtrees

Several characteristic parameters of randomly grown quadtrees of any dimension are analysed. Additive parameters have expectations whose generating functions are expressible in terms of generalized hypergeometric functions. A complex asymptotic process based on singularity analysis and integral representations akin to Mellin transforms leads to explicit values for various structure constants related to path length, retrieval costs, and storage occupation. Hyperg eometriques et structure de co^ ut des arbres quadrants R esum e. Plusieurs caract eristiques fondamentales des arbres quadrants obtenus par croissance al eatoire sont analys ees. Les param etres additifs ont des esp erances dont les s eries g en eratrices s'expriment en terme de fonctions hyperg eom etriques. Un proc ed e d'analyse asymptotique com-plexe fond e sur l'analyse de singularit e et sur des repr esentations int egrales apparent ees a la transformation de Mellin conduit a des formes explicites pour diverses constantes de structure associ ees a la longueur de cheminement, au co^ ut de recherche, ou a l'occupation m emoire. Abstract. Several characteristic parameters of randomly grown quadtrees of any dimension are analysed. Additive parameters have expectations whose generating functions are expressible in terms of generalized hypergeometric functions. A complex asymptotic process based on singularity analysis and integral representations akin to Mellin transforms leads to explicit values for various structure constants related to path length, retrieval costs, and storage occupation.