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A company has a number of offices and wants to design a communications network l...

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A company has a number of offices and wants to design a communications network linking them. For certain pairs (v,w) of offices, it is feasible to build a direct link joining v and w, and there is a known (positive) cost cv w incurred if link vw is built. The company wants to construct enough direct links so that every pair of offices can communicate (perhaps indirectly). Subject to this condition, the company would like to minimize the total construction cost. An appropriate problem similar to this one whose algorithm can be used to solve this problem is (mention the name of the algorithm for the problem-if one exists, in the justification):

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