Jeremy Ting edited q3.tex  almost 10 years ago

Commit id: aa2aab99e6171a07b9e58f3b404611129d922e47

deletions | additions      

       

So the number of edges that cross A and B = sum of the number of edges added by the $End$ nodes...  Which is replace_contentgt;=\sum\limits_{i=1}^n $\sum\limits_{i=1}^n  \frac{e_i}{2} = E$ (since this is how much the greedy algorithm adds each time)... Which is replace_contentgt;= \frac{E}{2}$ (since $\frac{E}{2}$ since  the sum of the $e_i$’s equal the total number of edges). edges.  So the number of edges that cross A and B from the greedy algo is replace_contentgt;= \frac{E}{2}$ $\frac{E}{2}$.  Since the optimal value can only be $E$ at best that means this greedy algorithm is at most 2 times worse than the optimal solution. \textbf{4.}