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3.3. Deterministic hierarchical consensus architectures
Serial DHCA Parallel DHCA
Dataset max (SRTDHCA) − min (SRTDHCA) max (PRTDHCA) − min (PRTDHCA)
(sec.) (%) (sec.) (%)
Zoo 7.36 547.6 0.08 42.3
Iris 5.34 707.4 0.12 53.2
Wine 12.66 636.8 0.23 70.1
Glass 8.78 387.1 0.34 90.8
Ionosphere 487.73 1650.3 2.82 92.3
WDBC 2095.36 1357.6 15.91 80.5
Balance 187.77 736.5 8.57 96.2
MFeat 16667.23 1562.4 1104.08 154.4
Table 3.9: Running time differences between the most and least computationally efficient
DHCA variants in both the serial and parallel implementations.
variant (following the strategy presented in table 3.6), and then i) estimate the running time
of flat consensus by extrapolating the execution times of the consensus processes conducted
upon mini-ensembles of size |dfi| (for i = {1,...,f}), or ii) launch the execution of flat
consensus, halting it as soon as its running time exceeds the estimated execution time of
the allegedly optimal DHCA variant —which is a simpler but less efficient alternative.
Summary of the most computationally efficient DHCA variants
To end this section, we have estimated which are the most computationally efficient consensus
architectures for the twelve unimodal data collections described in appendix A.2.1.
The results corresponding to the fully serial and parallel implementations are presented in
tables 3.10 and 3.11, respectively.
As regards the serial consensus architecture implementation (table 3.10), a few notational
observations must be made: successful predictions of the computationally optimal
consensus architecture (i.e. the minima of SERTDHCA and SRTDHCA are yielded by the
same consensus architecture) are denoted with a dagger (†). Moreover, we highlight the
cases where the minimum time complexity consensus architecture is the DHCA variant defined
by the ordered list of diversity factors arranged in decreasing cardinality order using
the double dagger (‡) symbol. Quite obviously, this only applies to the first eight data
collections (Zoo to MFeat), as in these cases both the estimated and real execution times
are available. For the remaining data sets (miniNG to PenDigits), we have only estimated
which are the computationally optimal consensus architectures.
Firstly, notice the large number of † symbols in table 3.10, which indicates the reasonably
high accuracy of the proposed optimal consensus architecture prediction methodology.
Moreover, notice that the most times we predict correctly that the least time consuming
consensus architecture is a DHCA variant, its architecture is created by arranging the
diversity factors in decreasing order of cardinality (which is denoted by the ‡ symbol).
Secondly, it is important to highlight that the higher the degree of diversity, the more
efficient DHCA variants become when compared to flat consensus —as already observed
throughout all the experiments reported, the EAC consensus function constitutes an exception
to this rule. However, notice that flat consensus tends to be computationally optimal
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