Question: Question 3: As input, we are given an undirected graph G = (V.E) and a set of tokens T, where |T| 2 E]. We have

Question 3: As input, we are given an undirected graph G

Question 3: As input, we are given an undirected graph G = (V.E) and a set of tokens T, where |T| 2 E]. We have to assign a token t(e) E T to every edge e E E in such a way that: for every tokent ET and every node v E V, at most 2 edges adjacent to the node u gets the token t. Our goal is to minimize the number of tokens in T that get assigned to at least one edge in E. Design a polynomial-time greedy algorithm for this problem, and derive an upper bound on its approxi- mation ratio. Try to ensure that the derived upper bound on the approximation ratio is as small as possible. [25 points) Question 3: As input, we are given an undirected graph G = (V.E) and a set of tokens T, where |T| 2 E]. We have to assign a token t(e) E T to every edge e E E in such a way that: for every tokent ET and every node v E V, at most 2 edges adjacent to the node u gets the token t. Our goal is to minimize the number of tokens in T that get assigned to at least one edge in E. Design a polynomial-time greedy algorithm for this problem, and derive an upper bound on its approxi- mation ratio. Try to ensure that the derived upper bound on the approximation ratio is as small as possible. [25 points)

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