-1
$\begingroup$

https://i.stack.imgur.com/qU6Fs.png

https://i.stack.imgur.com/huQxq.png

How do I prove the correctness of this algorithm?

$\endgroup$
2
  • 1
    $\begingroup$ What are your thoughts? Have you made any progress on this problem? Do you have any ideas at all? $\endgroup$ – Yuval Filmus Oct 21 '20 at 14:05
  • $\begingroup$ cs.stackexchange.com/q/59964/755 $\endgroup$ – D.W. Oct 22 '20 at 3:53
0
$\begingroup$

Desicion of Algorithms : $ T_{1},T_{2},....,T_{i}$ , cost $ C = C_{1},C_2,....,C_i$

$ \frac{Algo}{Opt} = \frac{C_1 + C_2 + ... + C_i}{(C_1/n_1)*n}$

and $ 4C_1 \geq C_k ,\forall 1 \leq k \leq m$

$ \implies \frac{C_1 + C_2 + ... + C_i}{(C_1/n_1) * n} \leq \frac{4iC_1}{(C_1/n_1)*n} = \frac{4in_1}{n}$

consider $ \frac{C_1}{n_1} \leq \frac{C_k}{n_k} \leq \frac{4C_1}{n_k} \implies n_k \leq 4n_1 $

$ \implies n_1 + n_2 + ... + n_{i-1} \leq n \implies 4(i - 1)n_1 \leq n \implies \frac{4in1}{n} \leq \frac{4n_1 + n}{n}$

$\frac{Algo}{Opt} \leq \frac{4in_1}{n} \leq \frac{4n_1 + n}{n} \leq \frac{4n_1 + n_1}{n_1} \leq 5 $

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.