Postman Problem

Here a carrier wants to travel the shortest distance through a neighborhood and return to his truck. Using a weighted graph for this network, the weight of each edge being its length, how can he 'walk the walk' over each edge but once? Or, more biologically speaking, how might carrier molecules such as hemoglobin cover the shortest distance through the circulation delivering oxygen to all points? Here we have many carriers in concert, but all should travel the least distance and avoid traversing too many paths more than once thus wasting heartbeat energy. Our weighted graph now corresponds to a circulatory network. For vertebrates evolution operating over millions of years discovered a closed circuit of minimal total weight that includes each edge at least and usually no more than once.

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