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is very small. This is true because credibility-based voting calculates credibility and de-
termine the redundancy supposing that the values of unknown parameters s and f are the
worst values ( f = f max etc.) to guarantee the reliability condition for any combination of
s and f . Therefore, in some cases where error rate is small, credibility-based voting may
perform redundant computation excessively and degrade the performance of VC systems,
as M -first voting with larger M does.
One of the solution to ease this performance degradation is focusing on job scheduling
methods of credibility-based voting. Since credibility-based voting with any scheduling
method guarantees the reliability condition, there is no drawback to use faster job schedul-
ing method (round robin method in this case). As shown in Fig.16 (b) and others, there is
a clear difference between the computation time of round robin method and that of random
method. Thus, we present a novel job scheduling method which enhances the performance
of credibility-based voting in the next section.
0.002
550
M-first(M=2)
M-first(M=3)
M-first with spot-checkin g (M=2)
M-first with spot-checking(M=3)
Credibility-based voting ( random)
Credibility-based voting(rr1)
ε acc
M-first(M=2)
M - f i r s t ( M = 3 )
M-first with spot-checking(M=2)
M-first with spot-checking(M=3)
Credibility-based voting(random)
Credibility-based voting(rr1)
500
0.0015
450
400
0.001
350
300
0.0005
250
0
200
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
1
c
c
(a) Error-rate
(b) Computation time T
Figure 17. M -first voting with spot-checking vs. Credibility-based voting for colluding rate
c ( acc =0.001 , s =0.1 , f =0.35 , q =0.1 , p d =0 , random scheduling with blacklisting).
Colluding rate c Fig.17 shows error rate and computation time of each method for col-
luding rate c in cases with blacklisting. Error rates of all methods increase with c , because
larger c increases the number of matching incorrect results and the probability of their being
final result. The value of c is also unknown to the master beforehand like s and f . Thus,
to guarantee the reliability condition for any c , the redundancy M should be set to a larger
value by supposing the worst case c =1 . Note that credibility-based voting guarantees the
reliability condition for any c . The computation times of spot-checking-based methods stay
constant for any c because almost all saboteurs are eliminated from the system regardless
the value of c .
Fig.18 shows error rate and computation time of each method in cases without black-
listing. This figure shows that the error rates of both 2 -first voting and 2 -FVSC exceed acc
when c ≥ 0.65 . The redundancy M should be set to larger than 3; however, such large
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