# 4 A region contains a number of towns connected by roads Each road

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4. A region contains a number of towns connected by
roads. Each road is labeled by the average number of
minutes required for a fire engine to travel to it. Each
intersection is labeled with a circle. Suppose that you work
for a city that has decided to place a fire station at location
G. (While this problem is small, you want to devise a
method to solve much larger problems).
(a) What algorithm would you recommend be used to find
the fastest route from the fire station to each of the
intersections? Demonstrate how it would work on the
example above if the fire station is placed at G. Show the
resulting routes.
(b) Suppose one optimal location (maybe instead of G)
must be selected for the fire station such that it minimizes
the distance to the farthest intersection. Devise an
algorithm to solve this problem given an arbitrary road
map. Analyze the time complexity of your algorithm when
there are f possible locations for the fire station (which
must be at one of the intersections) and r possible roads.
(c) In the above graph what is the optimal location to
place the fire station? Why?
Solution
a)

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4. A region contains a number of towns connected by roads. Each road is labeled by the average number of minutes required for a fire engine to travel to it. Each intersection is labeled with a circle. Suppose that you work for a city that has decided to place a fire station at location G. (While this problem is small, you want to devise a method to solve much larger problems). (a) What algorithm would you recommend be used to find the fastest route from the fire station to each of the intersections? Demonstrate how it would work on the example above if the fire station is placed at G. Show the ...
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