SF d k it T n e 0 mP n c F M Para-Sport Sprint B S tS i t MPa a p r S Tandem, Q W Sprint, QF W T d QWS i t QFW
n e , WS r W Sprint S i t 16:00 -19:30 1600 19 30 600- : 0 F M Para-Sport Sprint B FMP S tS i tB FM a -p t p n B Tandem, 1000m Time Trial, T d 1000 Ti T i l n em 00 me 40km Points Race, SF W 40k P i t R SFW 4 k o e S W Sprint, F W Sprint (5th-8th), 10km Scratch Race.
Contents 1 Introduction 259 2 The results 263 3 Sketch of the proof of the results for QFW 264 3.
For QFW the cost of one merging step is thus given by the minimum of the class sizes min(N[s], N[t]), whereas for QF the cost is given by N[s] or N[t] with equal probability 1/2.
The QFW algorithm under the random spanning tree model is illustrated by an example in Figure 1.
The algorithms QFW and QF have been analyzed first by (Yao76) and (KS78) for both models described above studying the expected value E([X.
For the algorithm QFW it has been conjectured in (CM04) a concentration result, namely that [X.
The aim of this paper is to describe the behavior of the total costs of the algorithms QFW and QFB for large n under the random spanning tree model by characterizing the limiting distribution of [X.
We only want to remark that the algorithms QFW and QF have a completely different behavior under the random graph model, which is a consequence of the analysis of (KS78) and (BS93) for the expected values of the total costs: E([X.