# GPS Navigation: Fastest, Shortest and Simplest.

All GPS navigation systems propose two options when it comes to route planning: the fastest and the shortest. The first one obviously targets minimum travel time, the second minimizes the distance travelled.

With real time traffic information the fastest option will change based on traffic conditions.

However, in general GPS navigators are not very intelligent when it comes to route planning and sometimes select non-intuitive options in order to reduce the length of the trip by a few hundred meteres or a few minutes. Often this happens at the price of more traffic lights, roundabouts or narrow roads. Sometimes, some sort of trade-off is performed.

But there is a third option. In fact, QCM technology allows to envisage a new, alternative option: Least Complex.

Consider the example below:

Of the three options – fastest, shortest and simplest (least complex) – only the shortest is invariant under traffic conditions. The other two change dynamically of course. What is not generally true is that the simplest route lies “between” the fastest and shortest. It may, in fact be longer than the shortest and may require more time than the fastest. From a mathematical point of view it may lie outside of the domain spanned by the previous two. In the example above, this corresponds to the dark blue option, with the light blue being the shortest.

The concept of least complex route has been proposed in a previous blog, where it has been suggested that travelling in complex terrain stresses (military) land vehicles (and troops) more than over simpler terrain. The concept may be extended to city traffic and driving, which in any case is frequently a stressful exercise.

From a mathematical point of view, finding the simplest path is easy with some clever pre-processing of real-time traffic data and road topology. In effect, with QCM it is possible to avoid entirely the issue of combinatorial optimization, which is a hard problem to solve if the number of options is large. Good taxi drivers can intuitively select the simplest route based on experience, intuition (gut feeling) and traffic conditions. And they can do it on the fly. Pretty much like the QCM, which is Artificial Intuition. Get the drift?