TESI DOCTORAL - La Salle

Chapter 3. Hierarchical consensus architectures
Serial DHCA
Dataset % correct ΔRT
predictions (sec.) (%)
Zoo 100 – –
Iris 96.4 0.01 1.2
Wine 89.3 0.69 16.2
Glass 92.9 0.09 5.4
Ionosphere 85.7 23.10 35.3
WDBC 92.9 2.03 2.2
Balance 75.0 1.12 17.1
MFeat 71.4 233.6 18.5
average 88.0 32.6 11.9
Table 3.8: Evaluation of the minimum complexity serial DHCA variant prediction based on
decreasing diversity factor ordering in terms of the percentage of correct predictions and
running time penalizations resulting from mistaken predictions.
correct predictions amounts to 233.6 seconds (a very high value due to the absolute real
execution times of hierarchical consensus architectures on this data set), which is equivalent
to an average deviation of 18.5% in relative percentage terms.
An averaging across data sets yields a prediction accuracy of 88%, i.e. it performs better
than the prediction methodology based on running time estimation, which made a 80% of
correct predictions (see table 3.7). This result reinforces the notion that the decreasing
cardinality diversity factor ordering approach to select the computationally optimal serial
DHCA variant is an alternative worth considering, as it requires no previous consensus
execution besides obtaining higher levels of prediction accuracy.
Aiming to support the conjecture that there is no computationally superior DHCA variant
when its fully parallel implementation is considered, we have conducted an experiment
seeking to quantify the differences between the least and most time consuming DHCA variants.
So as to provide a valid contrast to these results, the same computation has been
conducted regarding the most and least computationally efficient serial DHCA variants,
proving that making an accurate selection is much more important in the serial than in the
parallel case. Table 3.9 presents the results obtained, averaged across all the experiments
conducted on each of the eight unimodal data collections.
It can be observed that the running time differences between the most and least computationally
efficient DHCA variants are very notable in the serial case —in fact, it takes from
5 to 18 times longer to run the slowest DHCA variant than the computationally optimal
one. In contrast, these variations are much smaller when the fully parallel implementation
of DHCA is considered. In this case, as expected, a greater running time uniformity is
observed across DHCA variants, as the least computationally efficient variant is at most 2.5
times slower than the fastest one.
To sum up, the decreasing cardinality diversity factor ordering provides the user with a
pretty accurate notion of which is the most computationally efficient DHCA configuration
without need of executing a single consensus process. However, this strategy does not allow
to decide whether the allegedly fastest DHCA variant is more efficient than flat consensus.
To do so, we propose estimating the running time of the computationally optimal DHCA
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