Question 3 (Primal-dual schema; 10 marks) The minimum multicut problem considers an edge weighted graph G and a set of vertex pairs {(s1, t1),..., (sk, tz)) and asks us to find an edge set CSE such that, for each 15i 0 has at most two edges in C. Show that this implies that and satisfy the 2-relaxed dual complementary slackness conditions (e) Conclude that the computed cut C must satisfy w(C) S 2 OPT Question 3 (Primal-dual schema; 10 marks) The minimum multicut problem considers an edge weighted graph G and a set of vertex pairs {(s1, t1),..., (sk, tz)) and asks us to find an edge set CSE such that, for each 15i 0 has at most two edges in C. Show that this implies that and satisfy the 2-relaxed dual complementary slackness conditions (e) Conclude that the computed cut C must satisfy w(C) S 2 OPT