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elkka · #10 05-02-2012, 04:38 AM

rohanag, the recursive bounds can easily be solved for $\varepsilon$ , as 1. they are, essentially, quadratic equations, and 2. only one root is of interest, as $\varepsilon$ >0. By solving the equations you get

(c) $\varepsilon = \frac{1}{N}+\sqrt{\frac{1}{N^2}+\frac{1}{N}\ln{\frac{6m_\mathcal{H}(2N)}{\delta}}};$

(d) $\varepsilon = \frac{1}{N-2}+\sqrt{\frac{1}{(N-2)^2}+\frac{1}{2(N-2)}\ln{\frac{4m_\mathcal{H}(N^2)}{\delta}}}.$