Exercise $2(2$ pts$)$

The picture on the right an instance of $\backslash ($ k $\backslash )-$CENTER where there are six nodes on the two$-$dimensional grid with the Manhattan distance between them $($see the note on the Manhattan distance at Blackboard, HW$-3$ in the assignment section$).$

$1.$ Taking $\backslash ($ k$=3\backslash ),$ use the greedy approximation algorithm to find three cluster centers and the corresponding clusters. Pick the node $\backslash ($ D $\backslash )$ as the first center. In the case of more than one choice, make either choice.

$2.$ Give any two traces that produce different solutions.