The analysis of find and versions of it - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2012

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.
Fichier principal
Vignette du fichier
729-7418-1-PB.pdf (403.24 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00990593 , version 1 (13-05-2014)

Identifiers

Cite

Diether Knof, Uwe Roesler. The analysis of find and versions of it. Discrete Mathematics and Theoretical Computer Science, 2012, Vol. 14 no. 2 (2), pp.129--154. ⟨10.46298/dmtcs.581⟩. ⟨hal-00990593⟩

Collections

TDS-MACS
103 View
1059 Download

Altmetric

Share

Gmail Facebook X LinkedIn More