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algorithm.design.kleinberg.tardos.solutions.ch2 (3)

# Algorithm Design

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Unformatted text preview: We know from the text that polynomials (i.e. a sum of terms where n is raised to ﬁxed powers, even if they are not integers) grow slower than exponentials. Thus, we will consider f1, f2, f3, f6 as a group, and then put f4 and f5 after them. For polynomials f, and fj, we know that f, and fj can be ordered by comparing the highest exponent on any term in f, to the highest exponent on any term in fj. Thus, we can put f2 before f3 before f1. Now, where to insert f6? It grows faster than H2, and from the text we know that logarithms grow slower than polynomials, so f6 grows slower than no for any C > 2. Thus we can insert f6 in this order between f3 and f1. Finally come f4 and 1%. We know that exponentials can be ordered by their bases, so we put f4 before f5. 1ex831.202.488 ...
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