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However, various problems exhibit very different computational properties, depending on how the runtime required for solving them is related to the fixed parameter chosen.
The runtime required for path identification can be limited to a specific number of iterations, in which case the solution is partial.
Simulation results show that: (i) the system protects users' privacy when they behave honestly, and penalizes selfish users; (ii) it supports a large number of users; (iii) the runtime required to group users is affordable; and (iv) groups are dynamic and their topology is unpredictable, which we argue that is positive from the privacy point of view.
For the three input networks in particular, the runtime required for exhaustive search (>5 h per gene per network) prohibits any further permutation procedures.
The second observation is that the runtime required by our algorithm was <2 seconds in all cases, whereas the algorithm by Bordewich and colleagues took a number of days in some cases, without completion.
We compared the runtime required by main memory and secondary memory-based implementations (Section "Secondary memory-based computation") of the RW algorithm described in Section "Local implementation of network-based algorithms".
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This contrasts with the much larger runtime required by the HMM-based methods; e.g. HAPAA takes around 7 h for each of the datasets described above (500 genotypes over 38 k SNPs) while SABER takes a little>2 h for a set of 4 k SNPs.
Table 5 shows the average per term runtime required to complete a 5-fold cross-validation on the Bacteria-net (17,638 nodes/proteins and more than 7 millions of edges).
Table 7 summarizes the average per-term runtime required to complete a 5-fold cross validation with the Eukarya-net involving more than 200,000 proteins of 13 multi-cellular eukarya organisms (Section "Eukarya-net").
Mugsy had the second fastest runtime, requiring <2 h for the alignment of 31 Streptococcus pneumoniae genomes and ~19 h for the alignment of 57 E.coli genomes (Table 2).
In this case, the reduced development time of the heuristic algorithm compared to other rule-based algorithms did not compensate for the long runtimes required to achieve similar accuracy.
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