So Dave is also a computer scientist
just like Alice, Bob, and Carol,
and he is working in Logistics,
and the problem that he is working on is
optimizing the delivery routes
for the mail trucks of his company.
So basically, the problem that Dave has to solve each day is the following:
Here's the headquarter of his company
where each day, the mail arrives,
so maybe the mail arrives by an airplane,
and that airplane delivers letters each day,
and then this delivery truck here
has to deliver those letters to all of the houses
that receive mail that day.
So let's say it's those 7 houses here where
this truck has to deliver the mail.
Now of course, the roads that connect the houses,
so not every house is connected to each other house directly,
and the roads also have different length,
and I'm going to specify this in minutes,
so if I write a 40 here, it means you need 40 minutes to get from
this house to this house,
and then 14 from this house to this house,
and 13 from this house to this house, and so on.
So you can already see that this looks very much like
a graph except that the edges now have
a certain distance or time attached to them.
Now the problem that Dave has to solve is a problem that we will call shortest tour.
We will say that as an optimization problem for now,
we will later work with the decision problem to show NP completeness of this problem.
The truck starts out here
at the headquarters,
and then, Dave is supposed to figure out
the fastest way for the truck to visit all houses
and then get back to the base, so it starts out here,
has to visit all houses.
It can visit a house more than once,
in case you're wondering, and then it has to get back to base.
So let's say the truck starts here
and let's say the first road it takes down is this one here.
What I would like you to tell me is
in which order should the truck
visit the other houses?
So this is the first house that the truck is visiting,
and I want you to enter a 2, 3, 4, 5, 6, and 7 here,
so if the house travels from House 1 to House 2 then to House 2 and so on,
it's taking the fastest possible route to visit all houses.
