One application of an Euler circuit is the well known postman problem. A postman (pedestrian) must deliver mail to every house along certain...

One application of an Euler circuit is the well known postman problem. A postman (pedestrian) must deliver mail to every house along certain designated streets. So it is necessary, in his postal circuit, that he traverse each street containing houses at least once. It would certainly be beneficial and less tiring if he were able to to designate a circuit where each street (path) is traversed exactly one time. If you were a postal employee about to deliver mail and you had to make a selection of one of various postal routes, what criteria would you use to make an optimal selection? How might you make use of the concept of the Euler circuit to influence your decision?