2n decreasing functions n n this second class of

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Unformatted text preview: 43 100" 7 520 128 2187 10 4106 1024 59049 12 16396 4096 531441 100000" 10000" g" 2^n" 3^n" 10" 1" 0" 2" 4" 6" 8" 10" 12" 14" g is linear on semi-log plot so exponential what base: compare to 2n, 3n 9 How about g? 2n 3n n g(n) 1 9 2 3 2 18 4 9 3 35 8 27 4 68 16 81 1000" 5 131 32 243 100" 7 520 128 2187 10 4106 1024 59049 12 16396 4096 531441 1000000" 100000" 10000" g" 2^n" 3^n" 10" 1" 0" 2" 4" 6" 8" 10" 12" 14" g: same slope as 2n, but shifted up, factor 4 so g(n) = 4.2n+ … Decreasing functions n༆  n༆  This second class of functions can be used to represent running times of programs as a function of the number of processors. Ideally, these functions decrease hyperbolically ¨༊  f(p) = c/p time to execute the program with p processors ¨༊  f(1) = c sequential time n༆  But this is hardly ever the case. One of the reasons for this is that programs have inherently sequential parts, that do not speed up with more processors: ¨༊  f...
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