TESI DOCTORAL - La Salle

3.2. Random hierarchical consensus architectures
which corresponds to an average across 50 independent runs of the experiments conducted
on each data collection.
It is to note that, as already observed in the experiment described in this section and
those presented in appendix C.2, SERTRHCA is a pretty accurate estimator of SRTRHCA
(despite being based on the running time of a single consensus) and, as such, it suceeds
notably in determining the most computationally efficient consensus architecture, achieving
an average level of accuracy superior to 78% across the eight data sets employed in these
experiments. In spite of this notably high accuracy percentage, notice that the resulting
running time increase derived from inaccurate predictions is pretty high when measured in
relative percentage —e.g. for the Zoo data set, the average running time of truly optimal
consensus architectures is more than doubled when suboptimal ones are selected. However,
if this average execution time increase is measured in absolute terms, we can conclude that
it is perfectly assumable from a practical viewpoint in most cases —after all, the large
relative deviation observed in the Zoo data collection results only in a one second running
time rise.
As regards the parallel implementation of the RHCA, there are a couple of issues worth
noting: firstly, the proposed prediction methodology performs worse than in the serial case.
This is due to the fact that, as observed across all the experiments conducted, PERTRHCA is
a poorer estimator of PRTRHCA. However, despite ΔRT achieves very high values in relative
terms, the absolute running time deviations between the truly and allegedly fastest consensus
architectures are, again, not of paramount importance (i.e. the running time overhead
due to a slightly erroneous estimation of the fastest RHCA variant clearly compensates the
hypothetical execution of the least efficient consensus architecture).
Recall that the proposed running time estimation methodology is based on capturing the
execution times of several (namely c) runs of the consensus process on mini-ensembles of the
sizes bij corresponding to each RHCA variant. As aforementioned, the results just reported
have been obtained upon a single execution (c = 1). But expectably, the larger the value
of c, the more accurate the estimation, but also the more costly in terms of computation
time.
So as to evaluate the influence of this factor, figure 3.8 depicts the evolution of the
percentage of correct predictions (for both the serial and parallel implementations, referred
to as %CPS and %CPP, respectively) and of the running time deviations (ΔRTS and ΔRTP
in both absolute and relative terms) as a function of the parameter c, varying its value
between 1 and 20, averaged across the eight data collections employed in this experiment.
It can be observed that, despite the relatively wide sweep of values of c, thevariation
in the percentage of correct predictions is below 6% for both the serial and parallel RHCA
implementations —see figure 3.8(a). In terms of the difference between the running times
of the truly and allegedly fastest consensus architectures, this results in a slight reduction
of ΔRTS and ΔRTP –figure 3.8(b)–, which is, in any case, lower than 1.7 seconds —which,
in relative percentage terms, amounts to a maximum reduction of 22% —see figure 3.8(c).
Thus, we can conclude that, despite being a coarse approximation, using the running
time of a single consensus process as the basis for estimating the execution time of the
whole RHCA yields pretty accurate results as far as the prediction of the most efficient
consensus architecture is concerned. Furthermore, when this prediction methodology fails,
the execution time overhead is, in most cases, not dramatic from a practical standpoint.
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