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 (use
Dykstra's) 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?
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4. A region contains a number of towns connected by roads. Each road is labeled by...