Problem $3$ You will be provided: Problem $3$ You will be provided:

Sample codes $($single file implementation in Python$)$ for Greedy I, II$,$ III;

Run at least $5$ graph instances $(30$ of them are provided$)$ for each size, $n=100,200,$

$300,400,500.$

Best$-$known results $($in terms of cut$-$value$)$ by L$2$A of those provided graph instances.

You are expected to report your results, which are close to the provided best$-$known results. Let

us use the metric gap $$ :

$=\frac{\text{b}\text{e}\text{s}\text{t}-\text{k}\text{n}\text{o}\text{w}\text{n}\text{c}\text{u}\text{t}-\text{v}\text{a}\text{l}\text{u}\text{e}-\text{y}\text{o}\text{u}\text{r}\text{c}\text{u}\text{t}-\text{v}\text{a}\text{l}\text{u}\text{e}}{\text{b}\text{e}\text{s}\text{t}-\text{k}\text{n}\text{o}\text{w}\text{n}\text{c}\text{u}\text{t}-\text{v}\text{a}\text{l}\text{u}\text{e}}100\%$

You are expected to:

revise the provided codes by adding your tricks.

run $($your revised$)$ codes $($you$)$ on the provided graph instances. Each student is

expected to play with graph instances with $n200.$

Your goal is to obtain a small $.$ Say

Inform Prof. Yanglet Xiaoyang Liu if your algorithm obtains $3\%$ comparing with L$2$A

algorithm's results, or if your results beat Gurobi's results.

Sample codes $($single file implementation in Python$)$ for Greedy I, II$,$ III;

Run at least $5$ graph instances $(30$ of them are provided$)$ for each size, n $=100,200,300,400,500.$

Best$-$known results $($in terms of cut$-$value$)$ by L$2$A of those provided graph instances.

You are expected to report your results, which are close to the provided best$-$known results. Let us use the metric gap :

$=$best$-$known cut$-$value $-$ your cut$-$valuebest$-$known cut$-$value$100\%$

You are expected to:

revise the provided codes by adding your tricks.

run $($your revised$)$ codes $($you$)$ on the provided graph instances. Each student is expected to play with graph instances with n $>=200.$

Your goal is to obtain a small $.$ Say

Inform Prof. Yanglet Xiaoyang Liu if your algorithm obtains comparing with L$2$A algorithm$$s results, or if your results beat Gurobi$$s results.