The objectives of navigation have, in the special case of air services, been summed up, in an ‘R.S.V.P.’ formula, as Regularity, Safety, Versatility and Punctuality. The formula holds for all navigation, since the object of every operator and every master is to carry his passenger or freight in safety on a preconceived time schedule, with virtually complete freedom of choice, by owner or master, of type of craft, of time of departure and of route. The enemies of this freedom of choice and of the preconceived schedule are almost wholly meteorological or astronomical; the only serious enemies are meteorological. The continuing concern of the ‘navigator’ proper is to avoid, detect and rectify departures from the preselected route and schedule. The whole task of ‘navigation’ is unfulfilled without an infallible look-out for dangerous obstacles, which may be at fixed and known absolute positions, or at random, variable and unknown positions relative to the craft. Good ‘eyes’ naturally or artificially aided and a good clock would be the only indispensable tools of whole navigation, were it not for those imperfections of the science and art of weather forecasting which leave the drift term in dead reckoning such a deplorably variable and unmanageable element in the dual problem of the navigator. That dual problem is ‘Where am I now?’ and ‘Where shall I be inxminutes from now?’ The unpredictability of the drift term and the imperfections of the navigator and his instruments prevent the answer to the second question emerging mechanically from the answers to the two much simpler and essentially similar questions: ‘Where am I now?’ and ‘Where was Iyminutes ago?’
A Randomly Weighted Minimum Arborescence with a Random Cost Constraint
