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L M$N
S
1000
11 12 13 14 15
0.8
relative frequency
log median number of backtracks
1 order order order order order
100
brelazs brelazr rbrelazs rbrelazr
0.6
0.4
10 0.2
1 0.1
0 0.2
0.3 0.4 0.5 fraction of pre-assigned elements
0.6
0.7
0
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5
10
15 20 25 30 35 40 number of backtracks for first solution
45
50
0.8
0.7
0.6
order order order order
relative frequency
1 12 13 14 15
fraction of unsolvable cases
0.8
0.6
0.5 brelazs brelazr rbrelazs rbrelazr
0.4
0.3
0.2
0.1 0.4 0 0 0.2
0 0
0.1
0.2
0.3 0.4 0.5 0.6 0.7 fraction of pre-assigned elements
0.8
0.9
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2
4 6 8 number of backtracks for first solution
10
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1
1 0.9
0.8
0.8
relative frequency
relative frequency
0.7 brelazs brelazr rbrelazs rbrelazr
0.6
0.4
brelazs brelazr rbrelazs rbrelazr
0.6 0.5 0.4 0.3
0.2
0.2 0.1
0 0
5
10
15 20 25 30 35 40 number of backtracks for first solution
45
50
0
0.5
500 1000 1500 number of backtracks for first solution
2000
0.6 brelazs brelazr rbrelazs rbrelazr
0.5
relative frequency
relative frequency
0.4
0.3
0.2
brelazs brelazr rbrelazs rbrelazr
0.4
0.3
0.2
0.1 0.1
0 0
2
4 6 8 number of backtracks for first solution
10
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0
2
4
6 8 10 12 14 16 number of backtracks for first solution
18
20
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1 0.98 brelazs brelazr rbrelazs rbrelazr
0.96
relative frequency
0.94 0.92 0.9 0.88 0.86
1
0.84 0.82
0.8
0.8 500
1000 1500 2000 number of backtracks for first solution
2500
0.7
3000
relative frequency
0
0.8
brelazs brelazr rbrelazs rbrelazr
0.7
0.6 relative frequency
brelazs rbrelazr
0.9
0.6 0.5 0.4 0.3 0.2
0.5 0.1 0.4 0
200
400 600 number of backtracks
800
1000
0.3 0.2 0.2
brelazs rbrelazr
median number of backtracks
0.1
0 0
2
4 6 8 number of backtracks for first solution
10
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0.15
0.1
0.05
0 0
50
100
150 200 number of backtracks
250
300
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Portfolio for 2 processors
Portfolio for 20 processors
1600
0.45 0 brelazs, 20 rbrelazr
2 brelazs, 0 rbrelazr 1400
expected number of backtracks
expected number of backtracks
0.4 1200
1000
800
600
400
0.35
0.3
0.25
0.2 1 brelazs, 1 rbrelazr
200
0 brelazs, 2 rbrelazr 20 brelazs, 0 rbrelazr 0.15 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52 standard deviation (risk)
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