3. Average distance(E)
• A university wanted to place two or more helpdesks
inside it’s campus(C) to serve its students during a
“Fest”.
• For this, the criteria for selection of such places
should take into account “the average distance(E)”
walked by a student to approach one of the
helpdesks.
4. One helpdesk
• The solution to this problem when only one helpdesk is allowed is
intuitive and trivial, the centroid of the campus.
7. #Helpdesks ≥ 2
• For campuses of circular, rectangular, or elliptical shapes the solution
for more than one is not obvious and our intuitions may mislead us.
• Moreover, the simultaneous equations that arise when to minimize
the average distance are not easily solvable.
• The problem gets much worse with the complexity in shape of the
campus. Hence, for now, we stick to convex shapes.
8. • Typical solutions for simple shapes have been
computed using iterative procedure.
• Later, in some specific cases, the results have helped
to get an insight into exact solutions.
9. Caution ::
Deriving critical point
conditions for E, in this case, is
not good for health.
Gradient-descent and Finite
Variation