Maximum Linear Arrangement:

Maximum Linear Arrangement problem.

in the first photo is the problem

in the second photo there is the algorithm provided to solve it

$1-$ does the algorithm achieves the required in the problem

if do please provide a full proof and guaratee of aproximation

please proove everything and dont just give direction

the proof should be clear and once again should explain every step

$2-$ if the algorithm does achieves the required

what is the complexity