PLEASD ANSWER 2 AND 4, (AND DOES 3 MAKE SENSE?),

PLEASE WRITE CLEARLY

Answer - 1

After to make the min. spanning tree, the first move in Christofides Algorithm is to detection all the M vertices with odd degree & detection a min. weight top matching for these odd vertices. N is even, so a bipartite matching is feasible.When the M odd-degree vertices are found it.

Min. weight perfect matching in a weighted bipartite graph. Let us beginning with assuming that we have an algorithm to detection the min-weight perfect matching.In the 1st segment of the lecture, we learn how to utilization this algorithm in solving another issue of weighted common graphs.In the 2nd segment, we discuss the algorithm itself.

Answer - 3

Not definite a priori.Static lodger issue.

2 n persons; every person ranks others from 1 to 2 n 1.

Assign lodger pairs so that no unsteady pairs.

A top matching is a matching that matches all vertices of the graph. That is, a matching is top if each vertex of the graph is event to an edge of the matching.Each top matching is max. & hence maximal.

2. Minimum weight matching / Odd vertices (M) , IN CHRISTOFIDES ALGORITHM 1. How to find the minimum weight matching for odd vertices? 2. How is the weight compared to the OPT route? 3. Why does such matching exist? 4. Remember, an approx algorithm for a NP-problem is useless if not done effectively. So, is it possible to find a min weight matching in polynomial time? 2. Minimum weight matching / Odd vertices (M) , IN CHRISTOFIDES ALGORITHM 1. How to find the minimum weight matching for odd vertices? 2. How is the weight compared to the OPT route? 3. Why does such matching exist? 4. Remember, an approx algorithm for a NP-problem is useless if not done effectively. So, is it possible to find a min weight matching in polynomial time