The analysis of find and versions of it

Abstract : In the running time analysis of the algorithm Find and versions of it appear as limiting distributions solutions of stochastic fixed points equation of the form X D = Sigma(i) AiXi o Bi + C on the space D of cadlag functions. The distribution of the D-valued process X is invariant by some random linear affine transformation of space and random time change. We show the existence of solutions in some generality via the Weighted Branching Process. Finite exponential moments are connected to stochastic fixed point of supremum type X D = sup(i) (A(i)X(i) + C-i) on the positive reals. Specifically we present a running time analysis of m-median and adapted versions of Find. The finite dimensional distributions converge in L-1 and are continuous in the cylinder coordinates. We present the optimal adapted version in the sense of low asymptotic average number of comparisons. The limit distribution of the optimal adapted version of Find is a point measure on the function [0, 1] there exists t -> 1 + mint, 1 - t.
Type de document :
Article dans une revue
Discrete Mathematics and Theoretical Computer Science, DMTCS, 2012, Vol. 14 no. 2 (2), pp.129--154
Liste complète des métadonnées

Littérature citée [25 références]  Voir  Masquer  Télécharger
Contributeur : Service Ist Inria Sophia Antipolis-Méditerranée / I3s <>
Soumis le : mardi 13 mai 2014 - 16:27:45
Dernière modification le : jeudi 7 septembre 2017 - 01:03:37
Document(s) archivé(s) le : lundi 10 avril 2017 - 22:50:11


Fichiers produits par l'(les) auteur(s)


  • HAL Id : hal-00990593, version 1



Diether Knof, Uwe Roesler. The analysis of find and versions of it. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2012, Vol. 14 no. 2 (2), pp.129--154. 〈hal-00990593〉



Consultations de la notice


Téléchargements de fichiers